Home » Physics » AP Physics 1 & 2 » Electric Fields & Forces

Dan Fullerton

Dan Fullerton

Electric Fields & Forces

Slide Duration:

Table of Contents

Section 1: Introduction
What is Physics?

7m 38s

Intro
0:00
Objectives
0:12
What is Physics?
0:31
What is Matter, Energy, and How to They Interact
0:55
Why?
0:58
Physics Answers the 'Why' Questions.
1:05
Matter
1:23
Matter
1:29
Mass
1:33
Inertial Mass
1:53
Gravitational Mass
2:12
A Spacecraft's Mass
2:58
Energy
3:37
Energy: The Ability or Capacity to Do Work
3:39
Work: The Process of Moving an Object
3:45
The Ability or Capacity to Move an Object
3:54
Mass-Energy Equivalence
4:51
Relationship Between Mass and Energy E=mc2
5:01
The Mass of An Object is Really a Measure of Its Energy
5:05
The Study of Everything
5:42
Introductory Course
6:19
Next Steps
7:15
Math Review

24m 12s

Intro
0:00
Outline
0:10
Objectives
0:28
Why Do We Need Units?
0:52
Need to Set Specific Standards for Our Measurements
1:01
Physicists Have Agreed to Use the Systeme International
1:24
The Systeme International
1:50
Based on Powers of 10
1:52
7 Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Kelvin, Mole
2:02
The Meter
2:18
Meter is a Measure of Length
2:20
Measurements Smaller than a Meter, Use: Centimeter, Millimeter, Micrometer, Nanometer
2:25
Measurements Larger Than a Meter, Use Kilometer
2:38
The Kilogram
2:46
Roughly Equivalent to 2.2 English Pounds
2:49
Grams, Milligrams
2:53
Megagram
2:59
Seconds
3:10
Base Unit of Time
3:12
Minute, Hour, Day
3:20
Milliseconds, Microseconds
3:33
Derived Units
3:41
Velocity
3:45
Acceleration
3:57
Force
4:04
Prefixes for Powers of 10
4:21
Converting Fundamental Units, Example 1
4:53
Converting Fundamental Units, Example 2
7:18
Two-Step Conversions, Example 1
8:24
Two-Step Conversions, Example 2
10:06
Derived Unit Conversions
11:29
Multi-Step Conversions
13:25
Metric Estimations
15:04
What are Significant Figures?
16:01
Represent a Manner of Showing Which Digits In a Number Are Known to Some Level of Certainty
16:03
Example
16:09
Measuring with Sig Figs
16:36
Rule 1
16:40
Rule 2
16:44
Rule 3
16:52
Reading Significant Figures
16:57
All Non-Zero Digits Are Significant
17:04
All Digits Between Non-Zero Digits Are Significant
17:07
Zeros to the Left of the Significant Digits
17:11
Zeros to the Right of the Significant Digits
17:16
Non-Zero Digits
17:21
Digits Between Non-Zeros Are Significant
17:45
Zeroes to the Right of the Sig Figs Are Significant
18:17
Why Scientific Notation?
18:36
Physical Measurements Vary Tremendously in Magnitude
18:38
Example
18:47
Scientific Notation in Practice
19:23
Example 1
19:28
Example 2
19:44
Using Scientific Notation
20:02
Show Your Value Using Correct Number of Significant Figures
20:05
Move the Decimal Point
20:09
Show Your Number Being Multiplied by 10 Raised to the Appropriate Power
20:14
Accuracy and Precision
20:23
Accuracy
20:36
Precision
20:41
Example 1: Scientific Notation w/ Sig Figs
21:48
Example 2: Scientific Notation - Compress
22:25
Example 3: Scientific Notation - Compress
23:07
Example 4: Scientific Notation - Expand
23:31
Vectors & Scalars

25m 5s

Intro
0:00
Objectives
0:05
Scalars
0:29
Definition of Scalar
0:39
Temperature, Mass, Time
0:45
Vectors
1:12
Vectors are Quantities That Have Magnitude and Direction
1:13
Represented by Arrows
1:31
Vector Representations
1:47
Graphical Vector Addition
2:42
Graphical Vector Subtraction
4:58
Vector Components
6:08
Angle of a Vector
8:22
Vector Notation
9:52
Example 1: Vector Components
14:30
Example 2: Vector Components
16:05
Example 3: Vector Magnitude
17:26
Example 4: Vector Addition
19:38
Example 5: Angle of a Vector
24:06
Section 2: Mechanics
Defining & Graphing Motion

30m 11s

Intro
0:00
Objectives
0:07
Position
0:40
An Object's Position Cab Be Assigned to a Variable on a Number Scale
0:43
Symbol for Position
1:07
Distance
1:13
When Position Changes, An Object Has Traveled Some Distance
1:14
Distance is Scalar and Measured in Meters
1:21
Example 1: Distance
1:34
Displacement
2:17
Displacement is a Vector Which Describes the Straight Line From Start to End Point
2:18
Measured in Meters
2:27
Example 2: Displacement
2:39
Average Speed
3:32
The Distance Traveled Divided by the Time Interval
3:33
Speed is a Scalar
3:47
Example 3: Average Speed
3:57
Average Velocity
4:37
The Displacement Divided by the Time Interval
4:38
Velocity is a Vector
4:53
Example 4: Average Velocity
5:06
Example 5: Chuck the Hungry Squirrel
5:55
Acceleration
8:02
Rate At Which Velocity Changes
8:13
Acceleration is a Vector
8:26
Example 6: Acceleration Problem
8:52
Average vs. Instantaneous
9:44
Average Values Take Into Account an Entire Time Interval
9:50
Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time
9:54
Example 7: Average Velocity
10:06
Particle Diagrams
11:57
Similar to the Effect of Oil Leak from a Car on the Pavement
11:59
Accelerating
13:03
Position-Time Graphs
14:17
Shows Position as a Function of Time
14:24
Slope of x-t Graph
15:08
Slope Gives You the Velocity
15:09
Negative Indicates Direction
16:27
Velocity-Time Graphs
16:45
Shows Velocity as a Function of Time
16:49
Area Under v-t Graphs
17:47
Area Under the V-T Graph Gives You Change in Displacement
17:48
Example 8: Slope of a v-t Graph
19:45
Acceleration-Time Graphs
21:44
Slope of the v-t Graph Gives You Acceleration
21:45
Area Under the a-t Graph Gives You an Object's Change in Velocity
22:24
Example 10: Motion Graphing
24:03
Example 11: v-t Graph
27:14
Example 12: Displacement From v-t Graph
28:14
Kinematic Equations

36m 13s

Intro
0:00
Objectives
0:07
Problem-Solving Toolbox
0:42
Graphs Are Not Always the Most Effective
0:47
Kinematic Equations Helps us Solve for Five Key Variables
0:56
Deriving the Kinematic Equations
1:29
Kinematic Equations
7:40
Problem Solving Steps
8:13
Label Your Horizontal or Vertical Motion
8:20
Choose a Direction as Positive
8:24
Create a Motion Analysis Table
8:33
Fill in Your Givens
8:42
Solve for Unknowns
8:45
Example 1: Horizontal Kinematics
8:51
Example 2: Vertical Kinematics
11:13
Example 3: 2 Step Problem
13:25
Example 4: Acceleration Problem
16:44
Example 5: Particle Diagrams
17:56
Example 6: Quadratic Solution
20:13
Free Fall
24:24
When the Only Force Acting on an Object is the Force of Gravity, the Motion is Free Fall
24:27
Air Resistance
24:51
Drop a Ball
24:56
Remove the Air from the Room
25:02
Analyze the Motion of Objects by Neglecting Air Resistance
25:06
Acceleration Due to Gravity
25:22
g = 9.8 m/s2
25:25
Approximate g as 10 m/s2 on the AP Exam
25:37
G is Referred to as the Gravitational Field Strength
25:48
Objects Falling From Rest
26:15
Objects Starting from Rest Have an Initial velocity of 0
26:19
Acceleration is +g
26:34
Example 7: Falling Objects
26:47
Objects Launched Upward
27:59
Acceleration is -g
28:04
At Highest Point, the Object has a Velocity of 0
28:19
Symmetry of Motion
28:27
Example 8: Ball Thrown Upward
28:47
Example 9: Height of a Jump
29:23
Example 10: Ball Thrown Downward
33:08
Example 11: Maximum Height
34:16
Projectiles

20m 32s

Intro
0:00
Objectives
0:06
What is a Projectile?
0:26
An Object That is Acted Upon Only By Gravity
0:29
Typically Launched at an Angle
0:43
Path of a Projectile
1:03
Projectiles Launched at an Angle Move in Parabolic Arcs
1:06
Symmetric and Parabolic
1:32
Horizontal Range and Max Height
1:49
Independence of Motion
2:17
Vertical
2:49
Horizontal
2:52
Example 1: Horizontal Launch
3:49
Example 2: Parabolic Path
7:41
Angled Projectiles
8:30
Must First Break Up the Object's Initial Velocity Into x- and y- Components of Initial Velocity
8:32
An Object Will Travel the Maximum Horizontal Distance with a Launch Angle of 45 Degrees
8:43
Example 3: Human Cannonball
8:55
Example 4: Motion Graphs
12:55
Example 5: Launch From a Height
15:33
Example 6: Acceleration of a Projectile
19:56
Relative Motion

10m 52s

Intro
0:00
Objectives
0:06
Reference Frames
0:18
Motion of an Observer
0:21
No Way to Distinguish Between Motion at Rest and Motion at a Constant Velocity
0:44
Motion is Relative
1:35
Example 1
1:39
Example 2
2:09
Calculating Relative Velocities
2:31
Example 1
2:43
Example 2
2:48
Example 3
2:52
Example 1
4:58
Example 2: Airspeed
6:19
Example 3: 2-D Relative Motion
7:39
Example 4: Relative Velocity with Direction
9:40
Newton's 1st Law of Motion

10m 16s

Intro
0:00
Objective
0:05
Newton's 1st Law of Motion
0:16
An Object At Rest Will Remain At Rest
0:21
An Object In Motion Will Remain in Motion
0:26
Net Force
0:39
Also Known As the Law of Inertia
0:46
Force
1:02
Push or Pull
1:04
Newtons
1:08
Contact and Field Forces
1:31
Contact Forces
1:50
Field Forces
2:11
What is a Net Force?
2:30
Vector Sum of All the Forces Acting on an Object
2:33
Translational Equilibrium
2:37
Unbalanced Force Is a Net Force
2:46
What Does It Mean?
3:49
An Object Will Continue in Its Current State of Motion Unless an Unbalanced Force Acts Upon It
3:50
Example of Newton's First Law
4:20
Objects in Motion
5:05
Will Remain in Motion At Constant Velocity
5:06
Hard to Find a Frictionless Environment on Earth
5:10
Static Equilibrium
5:40
Net Force on an Object is 0
5:44
Inertia
6:21
Tendency of an Object to Resist a Change in Velocity
6:23
Inertial Mass
6:35
Gravitational Mass
6:40
Example 1: Inertia
7:10
Example 2: Inertia
7:37
Example 3: Translational Equilibrium
8:03
Example 4: Net Force
8:40
Newton's 2nd Law of Motion

34m 55s

Intro
0:00
Objective
0:07
Free Body Diagrams
0:37
Tools Used to Analyze Physical Situations
0:40
Show All the Forces Acting on a Single Object
0:45
Drawing FBDs
0:58
Draw Object of Interest as a Dot
1:00
Sketch a Coordinate System
1:10
Example 1: Falling Elephant
1:18
Example 2: Falling Elephant with Air Resistance
2:07
Example 3: Soda on Table
3:00
Example 4: Box in Equilibrium
4:25
Example 5: Block on a Ramp
5:01
Pseudo-FBDs
5:53
Draw When Forces Don't Line Up with Axes
5:56
Break Forces That Don’t Line Up with Axes into Components That Do
6:00
Example 6: Objects on a Ramp
6:32
Example 7: Car on a Banked Turn
10:23
Newton's 2nd Law of Motion
12:56
The Acceleration of an Object is in the Direction of the Directly Proportional to the Net Force Applied
13:06
Newton's 1st Two Laws Compared
13:45
Newton's 1st Law
13:51
Newton's 2nd Law
14:10
Applying Newton's 2nd Law
14:50
Example 8: Applying Newton's 2nd Law
15:23
Example 9: Stopping a Baseball
16:52
Example 10: Block on a Surface
19:51
Example 11: Concurrent Forces
21:16
Mass vs. Weight
22:28
Mass
22:29
Weight
22:47
Example 12: Mass vs. Weight
23:16
Translational Equilibrium
24:47
Occurs When There Is No Net Force on an Object
24:49
Equilibrant
24:57
Example 13: Translational Equilibrium
25:29
Example 14: Translational Equilibrium
26:56
Example 15: Determining Acceleration
28:05
Example 16: Suspended Mass
31:03
Newton's 3rd Law of Motion

5m 58s

Intro
0:00
Objectives
0:06
Newton's 3rd Law of Motion
0:20
All Forces Come in Pairs
0:24
Examples
1:22
Action-Reaction Pairs
2:07
Girl Kicking Soccer Ball
2:11
Rocket Ship in Space
2:29
Gravity on You
2:53
Example 1: Force of Gravity
3:34
Example 2: Sailboat
4:00
Example 3: Hammer and Nail
4:49
Example 4: Net Force
5:06
Friction

17m 49s

Intro
0:00
Objectives
0:06
Examples
0:23
Friction Opposes Motion
0:24
Kinetic Friction
0:27
Static Friction
0:36
Magnitude of Frictional Force Is Determined By Two Things
0:41
Coefficient Friction
2:27
Ratio of the Frictional Force and the Normal Force
2:28
Chart of Different Values of Friction
2:48
Kinetic or Static?
3:31
Example 1: Car Sliding
4:18
Example 2: Block on Incline
5:03
Calculating the Force of Friction
5:48
Depends Only Upon the Nature of the Surfaces in Contact and the Magnitude of the Force
5:50
Terminal Velocity
6:14
Air Resistance
6:18
Terminal Velocity of the Falling Object
6:33
Example 3: Finding the Frictional Force
7:36
Example 4: Box on Wood Surface
9:13
Example 5: Static vs. Kinetic Friction
11:49
Example 6: Drag Force on Airplane
12:15
Example 7: Pulling a Sled
13:21
Dynamics Applications

35m 27s

Intro
0:00
Objectives
0:08
Free Body Diagrams
0:49
Drawing FBDs
1:09
Draw Object of Interest as a Dot
1:12
Sketch a Coordinate System
1:18
Example 1: FBD of Block on Ramp
1:39
Pseudo-FBDs
1:59
Draw Object of Interest as a Dot
2:00
Break Up the Forces
2:07
Box on a Ramp
2:12
Example 2: Box at Rest
4:28
Example 3: Box Held by Force
5:00
What is an Atwood Machine?
6:46
Two Objects are Connected by a Light String Over a Mass-less Pulley
6:49
Properties of Atwood Machines
7:13
Ideal Pulleys are Frictionless and Mass-less
7:16
Tension is Constant in a Light String Passing Over an Ideal Pulley
7:23
Solving Atwood Machine Problems
8:02
Alternate Solution
12:07
Analyze the System as a Whole
12:12
Elevators
14:24
Scales Read the Force They Exert on an Object Placed Upon Them
14:42
Can be Used to Analyze Using Newton's 2nd Law and Free body Diagrams
15:23
Example 4: Elevator Accelerates Upward
15:36
Example 5: Truck on a Hill
18:30
Example 6: Force Up a Ramp
19:28
Example 7: Acceleration Down a Ramp
21:56
Example 8: Basic Atwood Machine
24:05
Example 9: Masses and Pulley on a Table
26:47
Example 10: Mass and Pulley on a Ramp
29:15
Example 11: Elevator Accelerating Downward
33:00
Impulse & Momentum

26m 6s

Intro
0:00
Objectives
0:06
Momentum
0:31
Example
0:35
Momentum measures How Hard It Is to Stop a Moving Object
0:47
Vector Quantity
0:58
Example 1: Comparing Momenta
1:48
Example 2: Calculating Momentum
3:08
Example 3: Changing Momentum
3:50
Impulse
5:02
Change In Momentum
5:05
Example 4: Impulse
5:26
Example 5: Impulse-Momentum
6:41
Deriving the Impulse-Momentum Theorem
9:04
Impulse-Momentum Theorem
12:02
Example 6: Impulse-Momentum Theorem
12:15
Non-Constant Forces
13:55
Impulse or Change in Momentum
13:56
Determine the Impulse by Calculating the Area of the Triangle Under the Curve
14:07
Center of Mass
14:56
Real Objects Are More Complex Than Theoretical Particles
14:59
Treat Entire Object as if Its Entire Mass Were Contained at the Object's Center of Mass
15:09
To Calculate the Center of Mass
15:17
Example 7: Force on a Moving Object
15:49
Example 8: Motorcycle Accident
17:49
Example 9: Auto Collision
19:32
Example 10: Center of Mass (1D)
21:29
Example 11: Center of Mass (2D)
23:28
Collisions

21m 59s

Intro
0:00
Objectives
0:09
Conservation of Momentum
0:18
Linear Momentum is Conserved in an Isolated System
0:21
Useful for Analyzing Collisions and Explosions
0:27
Momentum Tables
0:58
Identify Objects in the System
1:05
Determine the Momenta of the Objects Before and After the Event
1:10
Add All the Momenta From Before the Event and Set Them Equal to Momenta After the Event
1:15
Solve Your Resulting Equation for Unknowns
1:20
Types of Collisions
1:31
Elastic Collision
1:36
Inelastic Collision
1:56
Example 1: Conservation of Momentum (1D)
2:02
Example 2: Inelastic Collision
5:12
Example 3: Recoil Velocity
7:16
Example 4: Conservation of Momentum (2D)
9:29
Example 5: Atomic Collision
16:02
Describing Circular Motion

7m 18s

Intro
0:00
Objectives
0:07
Uniform Circular Motion
0:20
Circumference
0:32
Average Speed Formula Still Applies
0:46
Frequency
1:03
Number of Revolutions or Cycles Which Occur Each Second
1:04
Hertz
1:24
Formula for Frequency
1:28
Period
1:36
Time It Takes for One Complete Revolution or Cycle
1:37
Frequency and Period
1:54
Example 1: Car on a Track
2:08
Example 2: Race Car
3:55
Example 3: Toy Train
4:45
Example 4: Round-A-Bout
5:39
Centripetal Acceleration & Force

26m 37s

Intro
0:00
Objectives
0:08
Uniform Circular Motion
0:38
Direction of ac
1:41
Magnitude of ac
3:50
Centripetal Force
4:08
For an Object to Accelerate, There Must Be a Net Force
4:18
Centripetal Force
4:26
Calculating Centripetal Force
6:14
Example 1: Acceleration
7:31
Example 2: Direction of ac
8:53
Example 3: Loss of Centripetal Force
9:19
Example 4: Velocity and Centripetal Force
10:08
Example 5: Demon Drop
10:55
Example 6: Centripetal Acceleration vs. Speed
14:11
Example 7: Calculating ac
15:03
Example 8: Running Back
15:45
Example 9: Car at an Intersection
17:15
Example 10: Bucket in Horizontal Circle
18:40
Example 11: Bucket in Vertical Circle
19:20
Example 12: Frictionless Banked Curve
21:55
Gravitation

32m 56s

Intro
0:00
Objectives
0:08
Universal Gravitation
0:29
The Bigger the Mass the Closer the Attraction
0:48
Formula for Gravitational Force
1:16
Calculating g
2:43
Mass of Earth
2:51
Radius of Earth
2:55
Inverse Square Relationship
4:32
Problem Solving Hints
7:21
Substitute Values in For Variables at the End of the Problem Only
7:26
Estimate the Order of Magnitude of the Answer Before Using Your Calculator
7:38
Make Sure Your Answer Makes Sense
7:55
Example 1: Asteroids
8:20
Example 2: Meteor and the Earth
10:17
Example 3: Satellite
13:13
Gravitational Fields
13:50
Gravity is a Non-Contact Force
13:54
Closer Objects
14:14
Denser Force Vectors
14:19
Gravitational Field Strength
15:09
Example 4: Astronaut
16:19
Gravitational Potential Energy
18:07
Two Masses Separated by Distance Exhibit an Attractive Force
18:11
Formula for Gravitational Field
19:21
How Do Orbits Work?
19:36
Example5: Gravitational Field Strength for Space Shuttle in Orbit
21:35
Example 6: Earth's Orbit
25:13
Example 7: Bowling Balls
27:25
Example 8: Freely Falling Object
28:07
Example 9: Finding g
28:40
Example 10: Space Vehicle on Mars
29:10
Example 11: Fg vs. Mass Graph
30:24
Example 12: Mass on Mars
31:14
Example 13: Two Satellites
31:51
Rotational Kinematics

15m 33s

Intro
0:00
Objectives
0:07
Radians and Degrees
0:26
In Degrees, Once Around a Circle is 360 Degrees
0:29
In Radians, Once Around a Circle is 2π
0:34
Example 1: Degrees to Radians
0:57
Example 2: Radians to Degrees
1:31
Linear vs. Angular Displacement
2:00
Linear Position
2:05
Angular Position
2:10
Linear vs. Angular Velocity
2:35
Linear Speed
2:39
Angular Speed
2:42
Direction of Angular Velocity
3:05
Converting Linear to Angular Velocity
4:22
Example 3: Angular Velocity Example
4:41
Linear vs. Angular Acceleration
5:36
Example 4: Angular Acceleration
6:15
Kinematic Variable Parallels
7:47
Displacement
7:52
Velocity
8:10
Acceleration
8:16
Time
8:22
Kinematic Variable Translations
8:30
Displacement
8:34
Velocity
8:42
Acceleration
8:50
Time
8:58
Kinematic Equation Parallels
9:09
Kinematic Equations
9:12
Delta
9:33
Final Velocity Squared and Angular Velocity Squared
9:54
Example 5: Medieval Flail
10:24
Example 6: CD Player
10:57
Example 7: Carousel
12:13
Example 8: Circular Saw
13:35
Torque

11m 21s

Intro
0:00
Objectives
0:05
Torque
0:18
Force That Causes an Object to Turn
0:22
Must be Perpendicular to the Displacement to Cause a Rotation
0:27
Lever Arm: The Stronger the Force, The More Torque
0:45
Direction of the Torque Vector
1:53
Perpendicular to the Position Vector and the Force Vector
1:54
Right-Hand Rule
2:08
Newton's 2nd Law: Translational vs. Rotational
2:46
Equilibrium
3:58
Static Equilibrium
4:01
Dynamic Equilibrium
4:09
Rotational Equilibrium
4:22
Example 1: Pirate Captain
4:32
Example 2: Auto Mechanic
5:25
Example 3: Sign Post
6:44
Example 4: See-Saw
9:01
Rotational Dynamics

36m 6s

Intro
0:00
Objectives
0:08
Types of Inertia
0:39
Inertial Mass (Translational Inertia)
0:42
Moment of Inertia (Rotational Inertia)
0:53
Moment of Inertia for Common Objects
1:48
Example 1: Calculating Moment of Inertia
2:53
Newton's 2nd Law - Revisited
5:09
Acceleration of an Object
5:15
Angular Acceleration of an Object
5:24
Example 2: Rotating Top
5:47
Example 3: Spinning Disc
7:54
Angular Momentum
9:41
Linear Momentum
9:43
Angular Momentum
10:00
Calculating Angular Momentum
10:51
Direction of the Angular Momentum Vector
11:26
Total Angular Momentum
12:29
Example 4: Angular Momentum of Particles
14:15
Example 5: Rotating Pedestal
16:51
Example 6: Rotating Discs
18:39
Angular Momentum and Heavenly Bodies
20:13
Types of Kinetic Energy
23:41
Objects Traveling with a Translational Velocity
23:45
Objects Traveling with Angular Velocity
24:00
Translational vs. Rotational Variables
24:33
Example 7: Kinetic Energy of a Basketball
25:45
Example 8: Playground Round-A-Bout
28:17
Example 9: The Ice Skater
30:54
Example 10: The Bowler
33:15
Work & Power

31m 20s

Intro
0:00
Objectives
0:09
What Is Work?
0:31
Power Output
0:35
Transfer Energy
0:39
Work is the Process of Moving an Object by Applying a Force
0:46
Examples of Work
0:56
Calculating Work
2:16
Only the Force in the Direction of the Displacement Counts
2:33
Formula for Work
2:48
Example 1: Moving a Refrigerator
3:16
Example 2: Liberating a Car
3:59
Example 3: Crate on a Ramp
5:20
Example 4: Lifting a Box
7:11
Example 5: Pulling a Wagon
8:38
Force vs. Displacement Graphs
9:33
The Area Under a Force vs. Displacement Graph is the Work Done by the Force
9:37
Find the Work Done
9:49
Example 6: Work From a Varying Force
11:00
Hooke's Law
12:42
The More You Stretch or Compress a Spring, The Greater the Force of the Spring
12:46
The Spring's Force is Opposite the Direction of Its Displacement from Equilibrium
13:00
Determining the Spring Constant
14:21
Work Done in Compressing the Spring
15:27
Example 7: Finding Spring Constant
16:21
Example 8: Calculating Spring Constant
17:58
Power
18:43
Work
18:46
Power
18:50
Example 9: Moving a Sofa
19:26
Calculating Power
20:41
Example 10: Motors Delivering Power
21:27
Example 11: Force on a Cyclist
22:40
Example 12: Work on a Spinning Mass
23:52
Example 13: Work Done by Friction
25:05
Example 14: Units of Power
28:38
Example 15: Frictional Force on a Sled
29:43
Energy

20m 15s

Intro
0:00
Objectives
0:07
What is Energy?
0:24
The Ability or Capacity to do Work
0:26
The Ability or Capacity to Move an Object
0:34
Types of Energy
0:39
Energy Transformations
2:07
Transfer Energy by Doing Work
2:12
Work-Energy Theorem
2:20
Units of Energy
2:51
Kinetic Energy
3:08
Energy of Motion
3:13
Ability or Capacity of a Moving Object to Move Another Object
3:17
A Single Object Can Only Have Kinetic Energy
3:46
Example 1: Kinetic Energy of a Motorcycle
5:08
Potential Energy
5:59
Energy An Object Possesses
6:10
Gravitational Potential Energy
7:21
Elastic Potential Energy
9:58
Internal Energy
10:16
Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration
10:20
Calculating Gravitational Potential Energy in a Constant Gravitational Field
10:57
Sources of Energy on Earth
12:41
Example 2: Potential Energy
13:41
Example 3: Energy of a System
14:40
Example 4: Kinetic and Potential Energy
15:36
Example 5: Pendulum
16:55
Conservation of Energy

23m 20s

Intro
0:00
Objectives
0:08
Law of Conservation of Energy
0:22
Energy Cannot Be Created or Destroyed.. It Can Only Be Changed
0:27
Mechanical Energy
0:34
Conservation Laws
0:40
Examples
0:49
Kinematics vs. Energy
4:34
Energy Approach
4:56
Kinematics Approach
6:04
The Pendulum
8:07
Example 1: Cart Compressing a Spring
13:09
Example 2
14:23
Example 3: Car Skidding to a Stop
16:15
Example 4: Accelerating an Object
17:27
Example 5: Block on Ramp
18:06
Example 6: Energy Transfers
19:21
Simple Harmonic Motion

58m 30s

Intro
0:00
Objectives
0:08
What Is Simple Harmonic Motion?
0:57
Nature's Typical Reaction to a Disturbance
1:00
A Displacement Which Results in a Linear Restoring Force Results in SHM
1:25
Review of Springs
1:43
When a Force is Applied to a Spring, the Spring Applies a Restoring Force
1:46
When the Spring is in Equilibrium, It Is 'Unstrained'
1:54
Factors Affecting the Force of A Spring
2:00
Oscillations
3:42
Repeated Motions
3:45
Cycle 1
3:52
Period
3:58
Frequency
4:07
Spring-Block Oscillator
4:47
Mass of the Block
4:59
Spring Constant
5:05
Example 1: Spring-Block Oscillator
6:30
Diagrams
8:07
Displacement
8:42
Velocity
8:57
Force
9:36
Acceleration
10:09
U
10:24
K
10:47
Example 2: Harmonic Oscillator Analysis
16:22
Circular Motion vs. SHM
23:26
Graphing SHM
25:52
Example 3: Position of an Oscillator
28:31
Vertical Spring-Block Oscillator
31:13
Example 4: Vertical Spring-Block Oscillator
34:26
Example 5: Bungee
36:39
The Pendulum
43:55
Mass Is Attached to a Light String That Swings Without Friction About the Vertical Equilibrium
44:04
Energy and the Simple Pendulum
44:58
Frequency and Period of a Pendulum
48:25
Period of an Ideal Pendulum
48:31
Assume Theta is Small
48:54
Example 6: The Pendulum
50:15
Example 7: Pendulum Clock
53:38
Example 8: Pendulum on the Moon
55:14
Example 9: Mass on a Spring
56:01
Section 3: Fluids
Density & Buoyancy

19m 48s

Intro
0:00
Objectives
0:09
Fluids
0:27
Fluid is Matter That Flows Under Pressure
0:31
Fluid Mechanics is the Study of Fluids
0:44
Density
0:57
Density is the Ratio of an Object's Mass to the Volume It Occupies
0:58
Less Dense Fluids
1:06
Less Dense Solids
1:09
Example 1: Density of Water
1:27
Example 2: Volume of Gold
2:19
Example 3: Floating
3:06
Buoyancy
3:54
Force Exerted by a Fluid on an Object, Opposing the Object's Weight
3:56
Buoyant Force Determined Using Archimedes Principle
4:03
Example 4: Buoyant Force
5:12
Example 5: Shark Tank
5:56
Example 6: Concrete Boat
7:47
Example 7: Apparent Mass
10:08
Example 8: Volume of a Submerged Cube
13:21
Example 9: Determining Density
15:37
Pressure & Pascal's Principle

18m 7s

Intro
0:00
Objectives
0:09
Pressure
0:25
Pressure is the Effect of a Force Acting Upon a Surface
0:27
Formula for Pressure
0:41
Force is Always Perpendicular to the Surface
0:50
Exerting Pressure
1:03
Fluids Exert Outward Pressure in All Directions on the Sides of Any Container Holding the Fluid
1:36
Earth's Atmosphere Exerts Pressure
1:42
Example 1: Pressure on Keyboard
2:17
Example 2: Sleepy Fisherman
3:03
Example 3: Scale on Planet Physica
4:12
Example 4: Ranking Pressures
5:00
Pressure on a Submerged Object
6:45
Pressure a Fluid Exerts on an Object Submerged in That Fluid
6:46
If There Is Atmosphere Above the Fluid
7:03
Example 5: Gauge Pressure Scuba Diving
7:27
Example 6: Absolute Pressure Scuba Diving
8:13
Pascal's Principle
8:51
Force Multiplication Using Pascal's Principle
9:24
Example 7: Barber's Chair
11:38
Example 8: Hydraulic Auto Lift
13:26
Example 9: Pressure on a Penny
14:41
Example 10: Depth in Fresh Water
16:39
Example 11: Absolute vs. Gauge Pressure
17:23
Continuity Equation for Fluids

7m

Intro
0:00
Objectives
0:08
Conservation of Mass for Fluid Flow
0:18
Law of Conservation of Mass for Fluids
0:21
Volume Flow Rate Remains Constant Throughout the Pipe
0:35
Volume Flow Rate
0:59
Quantified In Terms Of Volume Flow Rate
1:01
Area of Pipe x Velocity of Fluid
1:05
Must Be Constant Throughout Pipe
1:10
Example 1: Tapered Pipe
1:44
Example 2: Garden Hose
2:37
Example 3: Oil Pipeline
4:49
Example 4: Roots of Continuity Equation
6:16
Bernoulli's Principle

20m

Intro
0:00
Objectives
0:08
Bernoulli's Principle
0:21
Airplane Wings
0:35
Venturi Pump
1:56
Bernoulli's Equation
3:32
Example 1: Torricelli's Theorem
4:38
Example 2: Gauge Pressure
7:26
Example 3: Shower Pressure
8:16
Example 4: Water Fountain
12:29
Example 5: Elevated Cistern
15:26
Section 4: Thermal Physics
Temperature, Heat, & Thermal Expansion

24m 17s

Intro
0:00
Objectives
0:12
Thermal Physics
0:42
Explores the Internal Energy of Objects Due to the Motion of the Atoms and Molecules Comprising the Objects
0:46
Explores the Transfer of This Energy From Object to Object
0:53
Temperature
1:00
Thermal Energy Is Related to the Kinetic Energy of All the Particles Comprising the Object
1:03
The More Kinetic Energy of the Constituent Particles Have, The Greater the Object's Thermal Energy
1:12
Temperature and Phases of Matter
1:44
Solids
1:48
Liquids
1:56
Gases
2:02
Average Kinetic Energy and Temperature
2:16
Average Kinetic Energy
2:24
Boltzmann's Constant
2:29
Temperature Scales
3:06
Converting Temperatures
4:37
Heat
5:03
Transfer of Thermal Energy
5:06
Accomplished Through Collisions Which is Conduction
5:13
Methods of Heat Transfer
5:52
Conduction
5:59
Convection
6:19
Radiation
6:31
Quantifying Heat Transfer in Conduction
6:37
Rate of Heat Transfer is Measured in Watts
6:42
Thermal Conductivity
7:12
Example 1: Average Kinetic Energy
7:35
Example 2: Body Temperature
8:22
Example 3: Temperature of Space
9:30
Example 4: Temperature of the Sun
10:44
Example 5: Heat Transfer Through Window
11:38
Example 6: Heat Transfer Across a Rod
12:40
Thermal Expansion
14:18
When Objects Are Heated, They Tend to Expand
14:19
At Higher Temperatures, Objects Have Higher Average Kinetic Energies
14:24
At Higher Levels of Vibration, The Particles Are Not Bound As Tightly to Each Other
14:30
Linear Expansion
15:11
Amount a Material Expands is Characterized by the Material's Coefficient of Expansion
15:14
One-Dimensional Expansion -> Linear Coefficient of Expansion
15:20
Volumetric Expansion
15:38
Three-Dimensional Expansion -> Volumetric Coefficient of Expansion
15:45
Volumetric Coefficient of Expansion is Roughly Three Times the Linear Coefficient of Expansion
16:03
Coefficients of Thermal Expansion
16:24
Example 7: Contracting Railroad Tie
16:59
Example 8: Expansion of an Aluminum Rod
18:37
Example 9: Water Spilling Out of a Glass
20:18
Example 10: Average Kinetic Energy vs. Temperature
22:18
Example 11: Expansion of a Ring
23:07
Ideal Gases

24m 15s

Intro
0:00
Objectives
0:10
Ideal Gases
0:25
Gas Is Comprised of Many Particles Moving Randomly in a Container
0:34
Particles Are Far Apart From One Another
0:46
Particles Do Not Exert Forces Upon One Another Unless They Come In Contact in an Elastic Collision
0:53
Ideal Gas Law
1:18
Atoms, Molecules, and Moles
2:56
Protons
2:59
Neutrons
3:15
Electrons
3:18
Examples
3:25
Example 1: Counting Moles
4:58
Example 2: Moles of CO2 in a Bottle
6:00
Example 3: Pressurized CO2
6:54
Example 4: Helium Balloon
8:53
Internal Energy of an Ideal Gas
10:17
The Average Kinetic Energy of the Particles of an Ideal Gas
10:21
Total Internal Energy of the Ideal Gas Can Be Found by Multiplying the Average Kinetic Energy of the Gas's Particles by the Numbers of Particles in the Gas
10:32
Example 5: Internal Energy of Oxygen
12:00
Example 6: Temperature of Argon
12:41
Root-Mean-Square Velocity
13:40
This is the Square Root of the Average Velocity Squared For All the Molecules in the System
13:43
Derived from the Maxwell-Boltzmann Distribution Function
13:56
Calculating vrms
14:56
Example 7: Average Velocity of a Gas
18:32
Example 8: Average Velocity of a Gas
19:44
Example 9: vrms of Molecules in Equilibrium
20:59
Example 10: Moles to Molecules
22:25
Example 11: Relating Temperature and Internal Energy
23:22
Thermodynamics

22m 29s

Intro
0:00
Objectives
0:06
Zeroth Law of Thermodynamics
0:26
First Law of Thermodynamics
1:00
The Change in the Internal Energy of a Closed System is Equal to the Heat Added to the System Plus the Work Done on the System
1:04
It is a Restatement of the Law of Conservation of Energy
1:19
Sign Conventions Are Important
1:25
Work Done on a Gas
1:44
Example 1: Adding Heat to a System
3:25
Example 2: Expanding a Gas
4:07
P-V Diagrams
5:11
Pressure-Volume Diagrams are Useful Tools for Visualizing Thermodynamic Processes of Gases
5:13
Use Ideal Gas Law to Determine Temperature of Gas
5:25
P-V Diagrams II
5:55
Volume Increases, Pressure Decreases
6:00
As Volume Expands, Gas Does Work
6:19
Temperature Rises as You Travel Up and Right on a PV Diagram
6:29
Example 3: PV Diagram Analysis
6:40
Types of PV Processes
7:52
Adiabatic
8:03
Isobaric
8:19
Isochoric
8:28
Isothermal
8:35
Adiabatic Processes
8:47
Heat Is not Transferred Into or Out of The System
8:50
Heat = 0
8:55
Isobaric Processes
9:19
Pressure Remains Constant
9:21
PV Diagram Shows a Horizontal Line
9:27
Isochoric Processes
9:51
Volume Remains Constant
9:52
PV Diagram Shows a Vertical Line
9:58
Work Done on the Gas is Zero
10:01
Isothermal Processes
10:27
Temperature Remains Constant
10:29
Lines on a PV Diagram Are Isotherms
10:31
PV Remains Constant
10:38
Internal Energy of Gas Remains Constant
10:40
Example 4: Adiabatic Expansion
10:46
Example 5: Removing Heat
11:25
Example 6: Ranking Processes
13:08
Second Law of Thermodynamics
13:59
Heat Flows Naturally From a Warmer Object to a Colder Object
14:02
Heat Energy Cannot be Completely Transformed Into Mechanical Work
14:11
All Natural Systems Tend Toward a Higher Level of Disorder
14:19
Heat Engines
14:52
Heat Engines Convert Heat Into Mechanical Work
14:56
Efficiency of a Heat Engine is the Ratio of the Engine You Get Out to the Energy You Put In
14:59
Power in Heat Engines
16:09
Heat Engines and PV Diagrams
17:38
Carnot Engine
17:54
It Is a Theoretical Heat Engine That Operates at Maximum Possible Efficiency
18:02
It Uses Only Isothermal and Adiabatic Processes
18:08
Carnot's Theorem
18:11
Example 7: Carnot Engine
18:49
Example 8: Maximum Efficiency
21:02
Example 9: PV Processes
21:51
Section 5: Electricity & Magnetism
Electric Fields & Forces

38m 24s

Intro
0:00
Objectives
0:10
Electric Charges
0:34
Matter is Made Up of Atoms
0:37
Protons Have a Charge of +1
0:45
Electrons Have a Charge of -1
1:00
Most Atoms Are Neutral
1:04
Ions
1:15
Fundamental Unit of Charge is the Coulomb
1:29
Like Charges Repel, While Opposites Attract
1:50
Example 1: Charge on an Object
2:22
Example 2: Charge of an Alpha Particle
3:36
Conductors and Insulators
4:27
Conductors Allow Electric Charges to Move Freely
4:30
Insulators Do Not Allow Electric Charges to Move Freely
4:39
Resistivity is a Material Property
4:45
Charging by Conduction
5:05
Materials May Be Charged by Contact, Known as Conduction
5:07
Conductors May Be Charged by Contact
5:24
Example 3: Charging by Conduction
5:38
The Electroscope
6:44
Charging by Induction
8:00
Example 4: Electrostatic Attraction
9:23
Coulomb's Law
11:46
Charged Objects Apply a Force Upon Each Other = Coulombic Force
11:52
Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges
12:04
Example 5: Determine Electrostatic Force
13:09
Example 6: Deflecting an Electron Beam
15:35
Electric Fields
16:28
The Property of Space That Allows a Charged Object to Feel a Force
16:44
Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge
17:01
The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force
17:24
Example 7: Field Between Metal Plates
17:58
Visualizing the Electric Field
19:27
Electric Field Lines Point Away from Positive Charges and Toward Negative Charges
19:40
Electric Field Lines Intersect Conductors at Right Angles to the Surface
19:50
Field Strength and Line Density Decreases as You Move Away From the Charges
19:58
Electric Field Lines
20:09
E Field Due to a Point Charge
22:32
Electric Fields Are Caused by Charges
22:35
Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law
22:38
To Find the Electric Field Due to Multiple Charges
23:09
Comparing Electricity to Gravity
23:56
Force
24:02
Field Strength
24:16
Constant
24:37
Charge/ Mass Units
25:01
Example 8: E Field From 3 Point Charges
25:07
Example 9: Where is the E Field Zero?
31:43
Example 10: Gravity and Electricity
36:38
Example 11: Field Due to Point Charge
37:34
Electric Potential Difference

35m 58s

Intro
0:00
Objectives
0:09
Electric Potential Energy
0:32
When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done
0:35
When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done
0:43
Electric Potential Difference
1:30
Example 1: Charge From Work
2:06
Example 2: Electric Energy
3:09
The Electron-Volt
4:02
Electronvolt (eV)
4:15
1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:28
Example 3: Energy in eV
5:33
Equipotential Lines
6:32
Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential
6:36
Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines
6:57
Drawing Equipotential Lines
8:15
Potential Due to a Point Charge
10:46
Calculate the Electric Field Vector Due to a Point Charge
10:52
Calculate the Potential Difference Due to a Point Charge
11:05
To Find the Potential Difference Due to Multiple Point Charges
11:16
Example 4: Potential Due to a Point Charge
11:52
Example 5: Potential Due to Point Charges
13:04
Parallel Plates
16:34
Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other
16:37
These Can Create a Capacitor
16:45
E Field Due to Parallel Plates
17:14
Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant
17:15
Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation
17:47
Capacitors
18:09
Electric Device Used to Store Charge
18:11
Once the Plates Are Charged, They Are Disconnected
18:30
Device's Capacitance
18:46
Capacitors Store Energy
19:28
Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other
19:31
Example 6: Capacitance
20:28
Example 7: Charge on a Capacitor
22:03
Designing Capacitors
24:00
Area of the Plates
24:05
Separation of the Plates
24:09
Insulating Material
24:13
Example 8: Designing a Capacitor
25:35
Example 9: Calculating Capacitance
27:39
Example 10: Electron in Space
29:47
Example 11: Proton Energy Transfer
30:35
Example 12: Two Conducting Spheres
32:50
Example 13: Equipotential Lines for a Capacitor
34:48
Current & Resistance

21m 14s

Intro
0:00
Objectives
0:06
Electric Current
0:19
Path Through Current Flows
0:21
Current is the Amount of Charge Passing a Point Per Unit Time
0:25
Conventional Current is the Direction of Positive Charge Flow
0:43
Example 1: Current Through a Resistor
1:19
Example 2: Current Due to Elementary Charges
1:47
Example 3: Charge in a Light Bulb
2:35
Example 4: Flashlights
3:03
Conductivity and Resistivity
4:41
Conductivity is a Material's Ability to Conduct Electric Charge
4:53
Resistivity is a Material's Ability to Resist the Movement of Electric Charge
5:11
Resistance vs. Resistivity vs. Resistors
5:35
Resistivity Is a Material Property
5:40
Resistance Is a Functional Property of an Element in an Electric Circuit
5:57
A Resistor is a Circuit Element
7:23
Resistors
7:45
Example 5: Calculating Resistance
8:17
Example 6: Resistance Dependencies
10:09
Configuration of Resistors
10:50
When Placed in a Circuit, Resistors Can be Organized in Both Serial and Parallel Arrangements
10:53
May Be Useful to Determine an Equivalent Resistance Which Could Be Used to Replace a System or Resistors with a Single Equivalent Resistor
10:58
Resistors in Series
11:15
Resistors in Parallel
12:35
Example 7: Finding Equivalent Resistance
15:01
Example 8: Length and Resistance
17:43
Example 9: Comparing Resistors
18:21
Example 10: Comparing Wires
19:12
Ohm's Law & Power

10m 35s

Intro
0:00
Objectives
0:06
Ohm's Law
0:21
Relates Resistance, Potential Difference, and Current Flow
0:23
Example 1: Resistance of a Wire
1:22
Example 2: Circuit Current
1:58
Example 3: Variable Resistor
2:30
Ohm's 'Law'?
3:22
Very Useful Empirical Relationship
3:31
Test if a Material is 'Ohmic'
3:40
Example 4: Ohmic Material
3:58
Electrical Power
4:24
Current Flowing Through a Circuit Causes a Transfer of Energy Into Different Types
4:26
Example: Light Bulb
4:36
Example: Television
4:58
Calculating Power
5:09
Electrical Energy
5:14
Charge Per Unit Time Is Current
5:29
Expand Using Ohm's Law
5:48
Example 5: Toaster
7:43
Example 6: Electric Iron
8:19
Example 7: Power of a Resistor
9:19
Example 8: Information Required to Determine Power in a Resistor
9:55
Circuits & Electrical Meters

8m 44s

Intro
0:00
Objectives
0:08
Electrical Circuits
0:21
A Closed-Loop Path Through Which Current Can Flow
0:22
Can Be Made Up of Most Any Materials, But Typically Comprised of Electrical Devices
0:27
Circuit Schematics
1:09
Symbols Represent Circuit Elements
1:30
Lines Represent Wires
1:33
Sources for Potential Difference: Voltaic Cells, Batteries, Power Supplies
1:36
Complete Conducting Paths
2:43
Voltmeters
3:20
Measure the Potential Difference Between Two Points in a Circuit
3:21
Connected in Parallel with the Element to be Measured
3:25
Have Very High Resistance
3:59
Ammeters
4:19
Measure the Current Flowing Through an Element of a Circuit
4:20
Connected in Series with the Circuit
4:25
Have Very Low Resistance
4:45
Example 1: Ammeter and Voltmeter Placement
4:56
Example 2: Analyzing R
6:27
Example 3: Voltmeter Placement
7:12
Example 4: Behavior or Electrical Meters
7:31
Circuit Analysis

48m 58s

Intro
0:00
Objectives
0:07
Series Circuits
0:27
Series Circuits Have Only a Single Current Path
0:29
Removal of any Circuit Element Causes an Open Circuit
0:31
Kirchhoff's Laws
1:36
Tools Utilized in Analyzing Circuits
1:42
Kirchhoff's Current Law States
1:47
Junction Rule
2:00
Kirchhoff's Voltage Law States
2:05
Loop Rule
2:18
Example 1: Voltage Across a Resistor
2:23
Example 2: Current at a Node
3:45
Basic Series Circuit Analysis
4:53
Example 3: Current in a Series Circuit
9:21
Example 4: Energy Expenditure in a Series Circuit
10:14
Example 5: Analysis of a Series Circuit
12:07
Example 6: Voltmeter In a Series Circuit
14:57
Parallel Circuits
17:11
Parallel Circuits Have Multiple Current Paths
17:13
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
17:15
Basic Parallel Circuit Analysis
18:19
Example 7: Parallel Circuit Analysis
21:05
Example 8: Equivalent Resistance
22:39
Example 9: Four Parallel Resistors
23:16
Example 10: Ammeter in a Parallel Circuit
26:27
Combination Series-Parallel Circuits
28:50
Look For Portions of the Circuit With Parallel Elements
28:56
Work Back to Original Circuit
29:09
Analysis of a Combination Circuit
29:20
Internal Resistance
34:11
In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'
34:16
Terminal Voltage of the Voltage Source is Reduced Slightly
34:25
Example 11: Two Voltage Sources
35:16
Example 12: Internal Resistance
42:46
Example 13: Complex Circuit with Meters
45:22
Example 14: Parallel Equivalent Resistance
48:24
RC Circuits

24m 47s

Intro
0:00
Objectives
0:08
Capacitors in Parallel
0:34
Capacitors Store Charge on Their Plates
0:37
Capacitors In Parallel Can Be Replaced with an Equivalent Capacitor
0:46
Capacitors in Series
2:42
Charge on Capacitors Must Be the Same
2:44
Capacitor In Series Can Be Replaced With an Equivalent Capacitor
2:47
RC Circuits
5:40
Comprised of a Source of Potential Difference, a Resistor Network, and One or More Capacitors
5:42
Uncharged Capacitors Act Like Wires
6:04
Charged Capacitors Act Like Opens
6:12
Charging an RC Circuit
6:23
Discharging an RC Circuit
11:36
Example 1: RC Analysis
14:50
Example 2: More RC Analysis
18:26
Example 3: Equivalent Capacitance
21:19
Example 4: More Equivalent Capacitance
22:48
Magnetic Fields & Properties

19m 48s

Intro
0:00
Objectives
0:07
Magnetism
0:32
A Force Caused by Moving Charges
0:34
Magnetic Domains Are Clusters of Atoms with Electrons Spinning in the Same Direction
0:51
Example 1: Types of Fields
1:23
Magnetic Field Lines
2:25
Make Closed Loops and Run From North to South Outside the Magnet
2:26
Magnetic Flux
2:42
Show the Direction the North Pole of a Magnet Would Tend to Point If Placed in the Field
2:54
Example 2: Lines of Magnetic Force
3:49
Example 3: Forces Between Bar Magnets
4:39
The Compass
5:28
The Earth is a Giant Magnet
5:31
The Earth's Magnetic North pole is Located Near the Geographic South Pole, and Vice Versa
5:33
A Compass Lines Up with the Net Magnetic Field
6:07
Example 3: Compass in Magnetic Field
6:41
Example 4: Compass Near a Bar Magnet
7:14
Magnetic Permeability
7:59
The Ratio of the Magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
8:02
Free Space
8:13
Highly Magnetic Materials Have Higher Values of Magnetic Permeability
8:34
Magnetic Dipole Moment
8:41
The Force That a Magnet Can Exert on Moving Charges
8:46
Relative Strength of a Magnet
8:54
Forces on Moving Charges
9:10
Moving Charges Create Magnetic Fields
9:11
Magnetic Fields Exert Forces on Moving Charges
9:17
Direction of the Magnetic Force
9:57
Direction is Given by the Right-Hand Rule
10:05
Right-Hand Rule
10:09
Mass Spectrometer
10:52
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
10:58
Used to Determine the Mass of an Unknown Particle
11:04
Velocity Selector
12:44
Mass Spectrometer with an Electric Field Added
12:47
Example 5: Force on an Electron
14:13
Example 6: Velocity of a Charged Particle
15:25
Example 7: Direction of the Magnetic Force
16:52
Example 8: Direction of Magnetic Force on Moving Charges
17:43
Example 9: Electron Released From Rest in Magnetic Field
18:53
Current-Carrying Wires

21m 29s

Intro
0:00
Objectives
0:09
Force on a Current-Carrying Wire
0:30
A Current-Carrying Wire in a Magnetic Field May Experience a Magnetic Force
0:33
Direction Given by the Right-Hand Rule
1:11
Example 1: Force on a Current-Carrying Wire
1:38
Example 2: Equilibrium on a Submerged Wire
2:33
Example 3: Torque on a Loop of Wire
5:55
Magnetic Field Due to a Current-Carrying Wire
8:49
Moving Charges Create Magnetic Fields
8:53
Wires Carry Moving Charges
8:56
Direction Given by the Right-Hand Rule
9:21
Example 4: Magnetic Field Due to a Wire
10:56
Magnetic Field Due to a Solenoid
12:12
Solenoid is a Coil of Wire
12:19
Direction Given by the Right-Hand Rule
12:47
Forces on 2 Parallel Wires
13:34
Current Flowing in the Same Direction
14:52
Current Flowing in Opposite Directions
14:57
Example 5: Magnetic Field Due to Wires
15:19
Example 6: Strength of an Electromagnet
18:35
Example 7: Force on a Wire
19:30
Example 8: Force Between Parallel Wires
20:47
Intro to Electromagnetic Induction

17m 26s

Intro
0:00
Objectives
0:09
Induced EMF
0:42
Charges Flowing Through a Wire Create Magnetic Fields
0:45
Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
0:49
Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
0:57
Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
1:17
Finding the Magnetic Flux
1:36
Magnetic Field Strength
1:39
Angle Between the Magnetic Field Strength and the Normal to the Area
1:51
Calculating Induced EMF
3:01
The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux
3:04
Induced EMF in a Rectangular Loop of Wire
4:03
Lenz's Law
5:17
Electric Generators and Motors
9:28
Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field
9:31
Generators Use Mechanical Energy to Turn the Coil of Wire
9:39
Electric Motor Operates Using Same Principle
10:30
Example 1: Finding Magnetic Flux
10:43
Example 2: Finding Induced EMF
11:54
Example 3: Changing Magnetic Field
13:52
Example 4: Current Induced in a Rectangular Loop of Wire
15:23
Section 6: Waves & Optics
Wave Characteristics

26m 41s

Intro
0:00
Objectives
0:09
Waves
0:32
Pulse
1:00
A Pulse is a Single Disturbance Which Carries Energy Through a Medium or Space
1:05
A Wave is a Series of Pulses
1:18
When a Pulse Reaches a Hard Boundary
1:37
When a Pulse Reaches a Soft or Flexible Boundary
2:04
Types of Waves
2:44
Mechanical Waves
2:56
Electromagnetic Waves
3:14
Types of Wave Motion
3:38
Longitudinal Waves
3:39
Transverse Waves
4:18
Anatomy of a Transverse Wave
5:18
Example 1: Waves Requiring a Medium
6:59
Example 2: Direction of Displacement
7:36
Example 3: Bell in a Vacuum Jar
8:47
Anatomy of a Longitudinal Wave
9:22
Example 4: Tuning Fork
9:57
Example 5: Amplitude of a Sound Wave
10:24
Frequency and Period
10:47
Example 6: Period of an EM Wave
11:23
Example 7: Frequency and Period
12:01
The Wave Equation
12:32
Velocity of a Wave is a Function of the Type of Wave and the Medium It Travels Through
12:36
Speed of a Wave is Related to Its Frequency and Wavelength
12:41
Example 8: Wavelength Using the Wave Equation
13:54
Example 9: Period of an EM Wave
14:35
Example 10: Blue Whale Waves
16:03
Sound Waves
17:29
Sound is a Mechanical Wave Observed by Detecting Vibrations in the Inner Ear
17:33
Particles of Sound Wave Vibrate Parallel With the Direction of the Wave's Velocity
17:56
Example 11: Distance from Speakers
18:24
Resonance
19:45
An Object with the Same 'Natural Frequency' May Begin to Vibrate at This Frequency
19:55
Classic Example
20:01
Example 12: Vibrating Car
20:32
Example 13: Sonar Signal
21:28
Example 14: Waves Across Media
24:06
Example 15: Wavelength of Middle C
25:24
Wave Interference

20m 45s

Intro
0:00
Objectives
0:09
Superposition
0:30
When More Than One Wave Travels Through the Same Location in the Same Medium
0:32
The Total Displacement is the Sum of All the Individual Displacements of the Waves
0:46
Example 1: Superposition of Pulses
1:01
Types of Interference
2:02
Constructive Interference
2:05
Destructive Interference
2:18
Example 2: Interference
2:47
Example 3: Shallow Water Waves
3:27
Standing Waves
4:23
When Waves of the Same Frequency and Amplitude Traveling in Opposite Directions Meet in the Same Medium
4:26
A Wave in Which Nodes Appear to be Standing Still and Antinodes Vibrate with Maximum Amplitude Above and Below the Axis
4:35
Standing Waves in String Instruments
5:36
Standing Waves in Open Tubes
8:49
Standing Waves in Closed Tubes
9:57
Interference From Multiple Sources
11:43
Constructive
11:55
Destructive
12:14
Beats
12:49
Two Sound Waves with Almost the Same Frequency Interfere to Create a Beat Pattern
12:52
A Frequency Difference of 1 to 4 Hz is Best for Human Detection of Beat Phenomena
13:05
Example 4
14:13
Example 5
18:03
Example 6
19:14
Example 7: Superposition
20:08
Wave Phenomena

19m 2s

Intro
0:00
Objective
0:08
Doppler Effect
0:36
The Shift In A Wave's Observed Frequency Due to Relative Motion Between the Source of the Wave and Observer
0:39
When Source and/or Observer Move Toward Each Other
0:45
When Source and/or Observer Move Away From Each Other
0:52
Practical Doppler Effect
1:01
Vehicle Traveling Past You
1:05
Applications Are Numerous and Widespread
1:56
Doppler Effect - Astronomy
2:43
Observed Frequencies Are Slightly Lower Than Scientists Would Predict
2:50
More Distant Celestial Objects Are Moving Away from the Earth Faster Than Nearer Objects
3:22
Example 1: Car Horn
3:36
Example 2: Moving Speaker
4:13
Diffraction
5:35
The Bending of Waves Around Obstacles
5:37
Most Apparent When Wavelength Is Same Order of Magnitude as the Obstacle/ Opening
6:10
Single-Slit Diffraction
6:16
Double-Slit Diffraction
8:13
Diffraction Grating
11:07
Sharper and Brighter Maxima
11:46
Useful for Determining Wavelengths Accurately
12:07
Example 3: Double Slit Pattern
12:30
Example 4: Determining Wavelength
16:05
Example 5: Radar Gun
18:04
Example 6: Red Shift
18:29
Light As a Wave

11m 35s

Intro
0:00
Objectives
0:14
Electromagnetic (EM) Waves
0:31
Light is an EM Wave
0:43
EM Waves Are Transverse Due to the Modulation of the Electric and Magnetic Fields Perpendicular to the Wave Velocity
1:00
Electromagnetic Wave Characteristics
1:37
The Product of an EM Wave's Frequency and Wavelength Must be Constant in a Vacuum
1:43
Polarization
3:36
Unpoloarized EM Waves Exhibit Modulation in All Directions
3:47
Polarized Light Consists of Light Vibrating in a Single Direction
4:07
Polarizers
4:29
Materials Which Act Like Filters to Only Allow Specific Polarizations of Light to Pass
4:33
Polarizers Typically Are Sheets of Material in Which Long Molecules Are Lined Up Like a Picket Fence
5:10
Polarizing Sunglasses
5:22
Reduce Reflections
5:26
Polarizing Sunglasses Have Vertical Polarizing Filters
5:48
Liquid Crystal Displays
6:08
LCDs Use Liquid Crystals in a Suspension That Align Themselves in a Specific Orientation When a Voltage is Applied
6:13
Cross-Orienting a Polarizer and a Matrix of Liquid Crystals so Light Can Be Modulated Pixel-by-Pixel
6:26
Example 1: Color of Light
7:30
Example 2: Analyzing an EM Wave
8:49
Example 3: Remote Control
9:45
Example 4: Comparing EM Waves
10:32
Reflection & Mirrors

24m 32s

Intro
0:00
Objectives
0:10
Waves at Boundaries
0:37
Reflected
0:43
Transmitted
0:45
Absorbed
0:48
Law of Reflection
0:58
The Angle of Incidence is Equal to the Angle of Reflection
1:00
They Are Both Measured From a Line Perpendicular, or Normal, to the Reflecting Surface
1:22
Types of Reflection
1:54
Diffuse Reflection
1:57
Specular Reflection
2:08
Example 1: Specular Reflection
2:24
Mirrors
3:20
Light Rays From the Object Reach the Plane Mirror and Are Reflected to the Observer
3:27
Virtual Image
3:33
Magnitude of Image Distance
4:05
Plane Mirror Ray Tracing
4:15
Object Distance
4:26
Image Distance
4:43
Magnification of Image
7:03
Example 2: Plane Mirror Images
7:28
Example 3: Image in a Plane Mirror
7:51
Spherical Mirrors
8:10
Inner Surface of a Spherical Mirror
8:19
Outer Surface of a Spherical Mirror
8:30
Focal Point of a Spherical Mirror
8:40
Converging
8:51
Diverging
9:00
Concave (Converging) Spherical Mirrors
9:09
Light Rays Coming Into a Mirror Parallel to the Principal Axis
9:14
Light Rays Passing Through the Center of Curvature
10:17
Light Rays From the Object Passing Directly Through the Focal Point
10:52
Mirror Equation (Lens Equation)
12:06
Object and Image Distances Are Positive on the Reflecting Side of the Mirror
12:13
Formula
12:19
Concave Mirror with Object Inside f
12:39
Example 4: Concave Spherical Mirror
14:21
Example 5: Image From a Concave Mirror
14:51
Convex (Diverging) Spherical Mirrors
16:29
Light Rays Coming Into a Mirror Parallel to the Principal Axis
16:37
Light Rays Striking the Center of the Mirror
16:50
Light Rays Never Converge on the Reflective Side of a Convex Mirror
16:54
Convex Mirror Ray Tracing
17:07
Example 6: Diverging Rays
19:12
Example 7: Focal Length
19:28
Example 8: Reflected Sonar Wave
19:53
Example 9: Plane Mirror Image Distance
20:20
Example 10: Image From a Concave Mirror
21:23
Example 11: Converging Mirror Image Distance
23:09
Refraction & Lenses

39m 42s

Intro
0:00
Objectives
0:09
Refraction
0:42
When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium
0:43
Wavelength Must Change If the Wave's Speed Changes
0:57
Refraction is When This Causes The Wave to Bend as It Enters the New Medium
1:12
Marching Band Analogy
1:22
Index of Refraction
2:37
Measure of How Much Light Slows Down in a Material
2:40
Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction
3:03
Indices of Refraction
3:21
Dispersion
4:01
White Light is Refracted Twice in Prism
4:23
Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency
4:41
Example 1: Determining n
5:14
Example 2: Light in Diamond and Crown Glass
5:55
Snell's Law
6:24
The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction
6:32
Light Bends Toward the Normal as it Enters a Material With a Higher n
7:08
Light Bends Toward the Normal as it Enters a Material With a Lower n
7:14
Example 3: Angle of Refraction
7:42
Example 4: Changes with Refraction
9:31
Total Internal Reflection
10:10
When the Angle of Refraction Reaches 90 Degrees
10:23
Critical Angle
10:34
Total Internal Reflection
10:51
Applications of TIR
12:13
Example 5: Critical Angle of Water
13:17
Thin Lenses
14:15
Convex Lenses
14:22
Concave Lenses
14:31
Convex Lenses
15:24
Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens
15:28
A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent
15:53
Example 6: Converging Lens Image
16:46
Example 7: Image Distance of Convex Lens
17:18
Concave Lenses
18:21
Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens
18:25
Concave Lenses Produce Upright, Virtual, Reduced Images
20:30
Example 8: Light Ray Thought a Lens
20:36
Systems of Optical Elements
21:05
Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element
21:16
Example 9: Lens and Mirrors
21:35
Thin Film Interference
27:22
When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film
27:25
If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere
27:31
Phase Change for Every Reflection from Low-Index to High-Index
28:09
Example 10: Thin Film Interference
28:41
Example 11: Wavelength in Diamond
32:07
Example 12: Light Incident on Crown Glass
33:57
Example 13: Real Image from Convex Lens
34:44
Example 14: Diverging Lens
35:45
Example 15: Creating Enlarged, Real Images
36:22
Example 16: Image from a Converging Lens
36:48
Example 17: Converging Lens System
37:50
Wave-Particle Duality

23m 47s

Intro
0:00
Objectives
0:11
Duality of Light
0:37
Photons
0:47
Dual Nature
0:53
Wave Evidence
1:00
Particle Evidence
1:10
Blackbody Radiation & the UV Catastrophe
1:20
Very Hot Objects Emitted Radiation in a Specific Spectrum of Frequencies and Intensities
1:25
Color Objects Emitted More Intensity at Higher Wavelengths
1:45
Quantization of Emitted Radiation
1:56
Photoelectric Effect
2:38
EM Radiation Striking a Piece of Metal May Emit Electrons
2:41
Not All EM Radiation Created Photoelectrons
2:49
Photons of Light
3:23
Photon Has Zero Mass, Zero Charge
3:32
Energy of a Photon is Quantized
3:36
Energy of a Photon is Related to its Frequency
3:41
Creation of Photoelectrons
4:17
Electrons in Metals Were Held in 'Energy Walls'
4:20
Work Function
4:32
Cutoff Frequency
4:54
Kinetic Energy of Photoelectrons
5:14
Electron in a Metal Absorbs a Photon with Energy Greater Than the Metal's Work Function
5:16
Electron is Emitted as a Photoelectron
5:24
Any Absorbed Energy Beyond That Required to Free the Electron is the KE of the Photoelectron
5:28
Photoelectric Effect in a Circuit
6:37
Compton Effect
8:28
Less of Energy and Momentum
8:49
Lost by X-Ray Equals Energy and Gained by Photoelectron
8:52
Compton Wavelength
9:09
Major Conclusions
9:36
De Broglie Wavelength
10:44
Smaller the Particle, the More Apparent the Wave Properties
11:03
Wavelength of a Moving Particle is Known as Its de Broglie Wavelength
11:07
Davisson-Germer Experiment
11:29
Verifies Wave Nature of Moving Particles
11:30
Shoot Electrons at Double Slit
11:34
Example 1
11:46
Example 2
13:07
Example 3
13:48
Example 4A
15:33
Example 4B
18:47
Example 5: Wave Nature of Light
19:54
Example 6: Moving Electrons
20:43
Example 7: Wavelength of an Electron
21:11
Example 8: Wrecking Ball
22:50
Section 7: Modern Physics
Atomic Energy Levels

14m 21s

Intro
0:00
Objectives
0:09
Rutherford's Gold Foil Experiment
0:35
Most of the Particles Go Through Undeflected
1:12
Some Alpha Particles Are Deflected Large Amounts
1:15
Atoms Have a Small, Massive, Positive Nucleus
1:20
Electrons Orbit the Nucleus
1:23
Most of the Atom is Empty Space
1:26
Problems with Rutherford's Model
1:31
Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons
1:39
Lose Energy When They Release Photons
1:46
Orbits Should Decay and They Should Be Unstable
1:50
Bohr Model of the Atom
2:09
Electrons Don't Lose Energy as They Accelerate
2:20
Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level
2:35
Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels
2:40
Energy Level Diagrams
3:29
n=1 is the Lowest Energy State
3:34
Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom
4:03
When Electron Reaches 0 eV It Is No Longer Bound
4:20
Electron Cloud Model (Probability Model)
4:46
Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus
4:53
Electron Orbitals Are Probability Regions
4:58
Atomic Spectra
5:16
Atoms Can Only Emit Certain Frequencies of Photons
5:19
Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels
5:34
This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element
5:37
Incandescence Emits a Continuous Energy
5:43
If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels
6:16
Continuous Spectrum
6:42
Absorption Spectrum
6:50
Emission Spectrum
7:08
X-Rays
7:36
The Photoelectric Effect in Reverse
7:38
Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate
7:53
Example 1: Electron in Hydrogen Atom
8:24
Example 2: EM Emission in Hydrogen
10:05
Example 3: Photon Frequencies
11:30
Example 4: Bright-Line Spectrum
12:24
Example 5: Gas Analysis
13:08
Nuclear Physics

15m 47s

Intro
0:00
Objectives
0:08
The Nucleus
0:33
Protons Have a Charge or +1 e
0:39
Neutrons Are Neutral (0 Charge)
0:42
Held Together by the Strong Nuclear Force
0:43
Example 1: Deconstructing an Atom
1:20
Mass-Energy Equivalence
2:06
Mass is a Measure of How Much Energy an Object Contains
2:16
Universal Conservation of Laws
2:31
Nuclear Binding Energy
2:53
A Strong Nuclear Force Holds Nucleons Together
3:04
Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus
3:19
Binding Energy of the Nucleus
3:32
Mass Defect
3:37
Nuclear Decay
4:30
Alpha Decay
4:42
Beta Decay
5:09
Gamma Decay
5:46
Fission
6:40
The Splitting of a Nucleus Into Two or More Nuclei
6:42
For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split
6:47
Fusion
8:14
The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus
8:15
This Fuels Our Sun and Stars
8:28
Basis of Hydrogen Bomb
8:31
Forces in the Universe
9:00
Strong Nuclear Force
9:06
Electromagnetic Force
9:13
Weak Nuclear Force
9:22
Gravitational Force
9:27
Example 2: Deuterium Nucleus
9:39
Example 3: Particle Accelerator
10:24
Example 4: Tritium Formation
12:03
Example 5: Beta Decay
13:02
Example 6: Gamma Decay
14:15
Example 7: Annihilation
14:39
Section 8: Sample AP Exams
AP Practice Exam: Multiple Choice, Part 1

38m 1s

Intro
0:00
Problem 1
1:33
Problem 2
1:57
Problem 3
2:50
Problem 4
3:46
Problem 5
4:13
Problem 6
4:41
Problem 7
6:12
Problem 8
6:49
Problem 9
7:49
Problem 10
9:31
Problem 11
10:08
Problem 12
11:03
Problem 13
11:30
Problem 14
12:28
Problem 15
14:04
Problem 16
15:05
Problem 17
15:55
Problem 18
17:06
Problem 19
18:43
Problem 20
19:58
Problem 21
22:03
Problem 22
22:49
Problem 23
23:28
Problem 24
24:04
Problem 25
25:07
Problem 26
26:46
Problem 27
28:03
Problem 28
28:49
Problem 29
30:20
Problem 30
31:10
Problem 31
33:03
Problem 32
33:46
Problem 33
34:47
Problem 34
36:07
Problem 35
36:44
AP Practice Exam: Multiple Choice, Part 2

37m 49s

Intro
0:00
Problem 36
0:18
Problem 37
0:42
Problem 38
2:13
Problem 39
4:10
Problem 40
4:47
Problem 41
5:52
Problem 42
7:22
Problem 43
8:16
Problem 44
9:11
Problem 45
9:42
Problem 46
10:56
Problem 47
12:03
Problem 48
13:58
Problem 49
14:49
Problem 50
15:36
Problem 51
15:51
Problem 52
17:18
Problem 53
17:59
Problem 54
19:10
Problem 55
21:27
Problem 56
22:40
Problem 57
23:19
Problem 58
23:50
Problem 59
25:35
Problem 60
26:45
Problem 61
27:57
Problem 62
28:32
Problem 63
29:52
Problem 64
30:27
Problem 65
31:27
Problem 66
32:22
Problem 67
33:18
Problem 68
35:21
Problem 69
36:27
Problem 70
36:46
AP Practice Exam: Free Response, Part 1

16m 53s

Intro
0:00
Question 1
0:23
Question 2
8:55
AP Practice Exam: Free Response, Part 2

9m 20s

Intro
0:00
Question 3
0:14
Question 4
4:34
AP Practice Exam: Free Response, Part 3

18m 12s

Intro
0:00
Question 5
0:15
Question 6
3:29
Question 7
6:18
Question 8
12:53
Section 9: Additional Examples
Metric Estimation

3m 53s

Intro
0:00
Question 1
0:38
Question 2
0:51
Question 3
1:09
Question 4
1:24
Question 5
1:49
Question 6
2:11
Question 7
2:27
Question 8
2:49
Question 9
3:03
Question 10
3:23
Defining Motion

7m 6s

Intro
0:00
Question 1
0:13
Question 2
0:50
Question 3
1:56
Question 4
2:24
Question 5
3:32
Question 6
4:01
Question 7
5:36
Question 8
6:36
Motion Graphs

6m 48s

Intro
0:00
Question 1
0:13
Question 2
2:01
Question 3
3:06
Question 4
3:41
Question 5
4:30
Question 6
5:52
Horizontal Kinematics

8m 16s

Intro
0:00
Question 1
0:19
Question 2
2:19
Question 3
3:16
Question 4
4:36
Question 5
6:43
Free Fall

7m 56s

Intro
0:00
Question 1-4
0:12
Question 5
2:36
Question 6
3:11
Question 7
4:44
Question 8
6:16
Projectile Motion

4m 17s

Intro
0:00
Question 1
0:13
Question 2
0:45
Question 3
1:25
Question 4
2:00
Question 5
2:32
Question 6
3:38
Newton's 1st Law

4m 34s

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0:15
Question 2
1:02
Question 3
1:50
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2:04
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2:26
Question 6
2:54
Question 7
3:11
Question 8
3:29
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3:47
Question 10
4:02
Newton's 2nd Law

5m 40s

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Question 2
0:55
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2:40
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3:33
Question 6
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Question 7
4:29
Newton's 3rd Law

3m 44s

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0:17
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Question 4
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Question 5
2:11
Question 6
2:29
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Friction

6m 37s

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0:47
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1:25
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2:26
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3:43
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4:41
Question 7
5:13
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Ramps and Inclines

6m 13s

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1:01
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3:11
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5:08
Circular Motion

5m 17s

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1:01
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2:33
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3:10
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3:31
Question 7
3:56
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4:33
Gravity

6m 33s

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1:05
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3:17
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4:41
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Momentum & Impulse

9m 29s

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4:28
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6:57
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7:47
Conservation of Momentum

9m 33s

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Work & Power

6m 2s

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0:29
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3:22
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Springs

7m 59s

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2:26
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3:37
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4:39
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5:28
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Energy & Energy Conservation

8m 47s

Intro
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1:27
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1:44
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2:33
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2:44
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3:33
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5:37
Question 10
7:12
Question 11
7:40
Electric Charge

7m 6s

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1:03
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3:01
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3:49
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4:24
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4:50
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5:32
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5:55
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6:26
Coulomb's Law

4m 13s

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0:14
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0:47
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1:25
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2:25
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3:01
Electric Fields & Forces

4m 11s

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0:51
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1:30
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2:19
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3:12
Electric Potential

5m 12s

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0:14
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0:42
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2:22
Question 6
2:49
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4:02
Electrical Current

6m 54s

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4:37
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4:59
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5:50
Resistance

5m 15s

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0:53
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3:21
Question 6
4:06
Ohm's Law

4m 27s

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0:33
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0:59
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3:19
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3:50
Circuit Analysis

6m 36s

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2:16
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3:18
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5:51
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6:00
Magnetism

3m 43s

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0:31
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1:19
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1:35
Question 6
2:36
Question 7
3:03
Wave Basics

4m 21s

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0:13
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0:36
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0:47
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1:13
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1:27
Question 6
1:39
Question 7
1:54
Question 8
2:22
Question 9
2:51
Question 10
3:32
Wave Characteristics

5m 33s

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0:23
Question 2
1:04
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2:01
Question 4
2:50
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3:12
Question 6
3:57
Question 7
4:16
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4:42
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4:56
Wave Behaviors

3m 52s

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0:40
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1:04
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1:17
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1:39
Question 6
2:07
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2:41
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3:09
Reflection

3m 48s

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0:50
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1:29
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1:46
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3:08
Refraction

2m 49s

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0:29
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1:03
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1:24
Question 7
2:01
Diffraction

2m 34s

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1:05
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1:37
Question 6
2:04
Electromagnetic Spectrum

7m 6s

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0:24
Question 2
0:39
Question 3
1:05
Question 4
1:51
Question 5
2:03
Question 6
2:58
Question 7
3:14
Question 8
3:52
Question 9
4:30
Question 10
5:04
Question 11
6:01
Question 12
6:16
Wave-Particle Duality

5m 30s

Intro
0:00
Question 1
0:15
Question 2
0:34
Question 3
0:53
Question 4
1:54
Question 5
2:16
Question 6
2:27
Question 7
2:42
Question 8
2:59
Question 9
3:45
Question 10
4:13
Question 11
4:33
Energy Levels

8m 13s

Intro
0:00
Question 1
0:25
Question 2
1:18
Question 3
1:43
Question 4
2:08
Question 5
3:17
Question 6
3:54
Question 7
4:40
Question 8
5:15
Question 9
5:54
Question 10
6:41
Question 11
7:14
Mass-Energy Equivalence

8m 15s

Intro
0:00
Question 1
0:19
Question 2
1:02
Question 3
1:37
Question 4
2:17
Question 5
2:55
Question 6
3:32
Question 7
4:13
Question 8
5:04
Question 9
5:29
Question 10
5:58
Question 11
6:48
Question 12
7:39
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Lecture Comments (28)

1 answer

Last reply by: Professor Dan Fullerton
Mon Feb 29, 2016 10:23 AM

Post by Sarmad Khokhar on February 29, 2016

In 6:02 how did you figured out that there would be positive charge ?

1 answer

Last reply by: Professor Dan Fullerton
Mon Feb 29, 2016 10:13 AM

Post by Sarmad Khokhar on February 29, 2016

Do we need to know questions that involve vector addition for coulomb's law in AP Physics 2 course ?

1 answer

Last reply by: Professor Dan Fullerton
Sun Feb 7, 2016 11:31 AM

Post by Gabrielle Martinez on February 6, 2016

I wonder why I can't find the " Electric Field Due to a Line of Charge" section.  I've attempted to search online on various sites for explanations and have not been successful.

1 answer

Last reply by: Professor Dan Fullerton
Mon Nov 23, 2015 7:17 AM

Post by Parth Shorey on November 16, 2015

Is the Q&A active?

1 answer

Last reply by: Professor Dan Fullerton
Sat Aug 15, 2015 2:35 PM

Post by Anh Dang on August 13, 2015

In example 5, so if it was repulsion instead, would the electrostatic force be negative?

1 answer

Last reply by: Professor Dan Fullerton
Thu Aug 13, 2015 5:24 PM

Post by Anh Dang on August 13, 2015

For the electroscope, why is it that when you touch the knob with a negative charge rod, you get a negative charge at the bottom of the leaves and the positive charge at the knob part?  Where did the positive charges come from?
And why , if reversed, when you put a positive charged rod to the knob, the whole metal part is positive without a negative charge at the knob?

1 answer

Last reply by: Professor Dan Fullerton
Sun Apr 12, 2015 4:49 PM

Post by Geoffrey Miller on April 12, 2015

Great lecture, Professor Fullerton. I have a question regarding example 5. Why is the answer positive and not negative 6.9*10^6? Is it because the force is a scaler in this instance?

2 answers

Last reply by: Hassan BIn Mazhar
Sat Oct 25, 2014 1:30 AM

Post by Hassan BIn Mazhar on October 23, 2014

Hello sir,I would like to ask u a question:If human body is a conductor and Earth is an infinite source of charge then would we have an electrostatic attraction from Earth as well?

1 answer

Last reply by: Professor Dan Fullerton
Sun May 25, 2014 11:05 AM

Post by Matej Neumann on May 25, 2014

Could the example 8 also be solved by using vectors? with the equation
E=k*q*r/r^3 and then adding all the j and i components together?

0 answers

Post by Madina Abdullah on May 5, 2014

Thank you Sir

1 answer

Last reply by: Professor Dan Fullerton
Sat Sep 7, 2013 5:48 PM

Post by Sam Mukau on September 7, 2013

for example 7, does the distance between the plates not matter? you did not use it in the calculation

1 answer

Last reply by: Professor Dan Fullerton
Sat Aug 31, 2013 12:50 PM

Post by Jude Nawlo on August 31, 2013

Also, in example 9, since both of the points are positive charges, why do they move in a direction towards each other if we know that like charges repel each other?

1 answer

Last reply by: Professor Dan Fullerton
Sat Aug 31, 2013 9:11 AM

Post by Jude Nawlo on August 31, 2013

For Example 3, I understand that the two conductors will distribute their charges equally, which result in both of them having four elementary charges. I understand the mathematical procedure of multiplying by 1.6 x 10^19 to get the charge of each. But I am confused about signs. If we are denoting the elementary charge as "e," then isn't that referring to an electron, and if so, why isn't the final charge of each conductor negative (since electrons are negative?)Or does the elementary charge refer to a positive or negative state or charge?

1 answer

Last reply by: Professor Dan Fullerton
Fri May 3, 2013 6:21 AM

Post by help me on May 2, 2013

Wonderful videos :) Thank you very much for starting your own Educator course. Very helpful, indeed.

Electric Fields & Forces

  • Matter has a property called resistivity, which relates to how easily electric charges move through the material.
  • Electric charge is conserved. Net charge is the sum of all charges of all objects in a system.
  • The smallest observed unit of charge that can be isolated is the elementary charge.
  • Electric force results from the interaction of two objects with electric charge.
  • The magnitude of the electric force (F) exerted on an object with charge q by an electric field E is F=qE.
  • The magnitude of the electric field vector is proportional to the net electric charge of the object(s) creating the field.
  • The electric field outside a spherically symmetric charged object is radial and follows an inverse square law as a function of the distance from the center of the object.
  • The electric field around dipoles and other systems of electrically charged objects is radial and follows an inverse square law as a function of the distance from the center of the object.
  • The electric field inside a conductor at equilibrium is zero.

Electric Fields & Forces

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  1. Intro
    • Objectives
      • Electric Charges
      • Example 1: Charge on an Object
        • Example 2: Charge of an Alpha Particle
          • Conductors and Insulators
          • Charging by Conduction
          • Example 3: Charging by Conduction
            • The Electroscope
              • Charging by Induction
                • Example 4: Electrostatic Attraction
                  • Coulomb's Law
                  • Example 5: Determine Electrostatic Force
                    • Example 6: Deflecting an Electron Beam
                      • Electric Fields
                      • Example 7: Field Between Metal Plates
                        • Visualizing the Electric Field
                        • Electric Field Lines
                          • E Field Due to a Point Charge
                          • Comparing Electricity to Gravity
                          • Example 8: E Field From 3 Point Charges
                            • Example 9: Where is the E Field Zero?
                              • Example 10: Gravity and Electricity
                                • Example 11: Field Due to Point Charge
                                  • Intro 0:00
                                  • Objectives 0:10
                                  • Electric Charges 0:34
                                    • Matter is Made Up of Atoms
                                    • Protons Have a Charge of +1
                                    • Electrons Have a Charge of -1
                                    • Most Atoms Are Neutral
                                    • Ions
                                    • Fundamental Unit of Charge is the Coulomb
                                    • Like Charges Repel, While Opposites Attract
                                  • Example 1: Charge on an Object 2:22
                                  • Example 2: Charge of an Alpha Particle 3:36
                                  • Conductors and Insulators 4:27
                                    • Conductors Allow Electric Charges to Move Freely
                                    • Insulators Do Not Allow Electric Charges to Move Freely
                                    • Resistivity is a Material Property
                                  • Charging by Conduction 5:05
                                    • Materials May Be Charged by Contact, Known as Conduction
                                    • Conductors May Be Charged by Contact
                                  • Example 3: Charging by Conduction 5:38
                                  • The Electroscope 6:44
                                  • Charging by Induction 8:00
                                  • Example 4: Electrostatic Attraction 9:23
                                  • Coulomb's Law 11:46
                                    • Charged Objects Apply a Force Upon Each Other = Coulombic Force
                                    • Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges
                                  • Example 5: Determine Electrostatic Force 13:09
                                  • Example 6: Deflecting an Electron Beam 15:35
                                  • Electric Fields 16:28
                                    • The Property of Space That Allows a Charged Object to Feel a Force
                                    • Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge
                                    • The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force
                                  • Example 7: Field Between Metal Plates 17:58
                                  • Visualizing the Electric Field 19:27
                                    • Electric Field Lines Point Away from Positive Charges and Toward Negative Charges
                                    • Electric Field Lines Intersect Conductors at Right Angles to the Surface
                                    • Field Strength and Line Density Decreases as You Move Away From the Charges
                                  • Electric Field Lines 20:09
                                  • E Field Due to a Point Charge 22:32
                                    • Electric Fields Are Caused by Charges
                                    • Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law
                                    • To Find the Electric Field Due to Multiple Charges
                                  • Comparing Electricity to Gravity 23:56
                                    • Force
                                    • Field Strength
                                    • Constant
                                    • Charge/ Mass Units
                                  • Example 8: E Field From 3 Point Charges 25:07
                                  • Example 9: Where is the E Field Zero? 31:43
                                  • Example 10: Gravity and Electricity 36:38
                                  • Example 11: Field Due to Point Charge 37:34

                                  Transcription: Electric Fields & Forces

                                  Hi everyone! We are thrilled to have you back with us here at Educator.com.0000

                                  Today we are going to start a lesson on electric fields and forces which is the beginning of our unit on electricity and magnetism.0003

                                  Our objectives are going to be to calculate the charge on an object and explain the Law of Conservation of Charge, describe differences between conductors and insulators, and explain the difference between conduction and induction.0010

                                  We will also use Coulomb's Law to solve for the force on a charged particle due to other point charges, calculate the electric field due to one or more point charges and finally to analyze electric field diagrams.0023

                                  Let us start by talking about electric charges.0034

                                  As you know matter is made up of atoms, and those atoms even have smaller particles -- subatomic particles such as protons, electrons and neutrons.0037

                                  Now protons have a charge of +1 and +1e is a +1 elementary charge, the smallest stable single charge, that is equal to 1.6 × 10-19 coulombs (C), the SI unit of charge.0045

                                  Electrons on the other hand have a charge of -1 elementary charge and neutrons are neutral.0060

                                  Now most atoms are neutral -- they have equal numbers of protons and electrons.0066

                                  The positives and the negatives balance out for a net charge of 0; it is neutral.0070

                                  But if an atom loses its electrons, loses an electron or two, it is going to become positively charged, or if it gains an electron or two, it is going to become negatively charged.0075

                                  We call those charged atoms 'ions'.0085

                                  Now the fundamental unit of charge in the SI system is the coulomb (C), and that is a big amount of isolated charge.0089

                                  The smallest isolated unit of electric charge is the elementary charge, 1e on a proton, -1e on an electron and it's magnitude is 1.6 × 10-19 C.0098

                                  Now like charges repel each other, opposites attract, and of course electric charge is conserved -- that is called the Law of Conservation of Charge.0110

                                  You cannot spontaneously have just a (+) charge appear.0119

                                  If you start off with 0 net charge, later on in a closed system you must still have 0 net charge.0122

                                  If you start off with 0 net charge you could have a +1e and a -1e so that your net is still 0, but you cannot spontaneously get a +3e and a -1e for a net of 2 -- charge has to be conserved.0127

                                  Now let us take a look at charge on an object.0143

                                  Mittens the cat possesses an excess of 6,000,000 electrons.0146

                                  Let us find the net charge on Mittens in coulombs SI units.0150

                                  Well charge gets the letter (Q) and that is going to be 6 × 106 electrons, and since they are negative I will put that there so we have -6 × 106 elementary charges...0154

                                  ...and we are going to try and convert that to coulombs and the way we are going to do that is by multiplying by 1 again -- that old trick.0168

                                  We want elementary charges to go away so I will put (e) down here and I want units of coulombs, so I will put that up here, and then I have to write numbers in here to make a ratio of 1.0175

                                  Well 1 elementary charge = 1.6 × 10-19 C.0186

                                  Now when I go through and do the math, my elementary charge units are going to cancel out and I will get -6 × 106 × 1.6 × 10-19 C for a total of -9.6 × 10-13 C as my answer. Great!0192

                                  Let us take a look at the charge of an alpha particle.0216

                                  An alpha particle, which is also known as a helium nucleus, consists of 2 protons and 2 neutrons, no electrons.0219

                                  So what is the charge of an alpha particle?0225

                                  Well if an alpha particle has 2 protons, those are the only charged particles, it must have a charge of +2 elementary charges.0228

                                  But let us convert that into coulombs -- +2 elementary charges, and we need to multiply that by 1, I will write 1 as 1e = 1.6 × 10-19 C...0239

                                  ...so I get a charge of 3.2 × 10-19 C when I put that into SI units -- 3.2 × 10-19.0254

                                  All right. As we talk about materials -- conductors are materials that allow charges to move freely.0268

                                  They have a very low resistivity, so charges can go through them very, very easily.0274

                                  Insulators, on the other hand, do not allow charges to move freely.0279

                                  They have what is known as a very high resistivity, and resistivity is a material property.0282

                                  If you look up the resistivity of gold, it has a certain value; if you look up the resistivity of glass, it has a specific value.0288

                                  It is a material property measured in ohm meters and it typically gets the symbol ρ, a squirrely little P.0296

                                  All right. Materials may be charged by contact known as conduction.0306

                                  You might have tried this trick before -- rub a balloon against your hair someday.0310

                                  Some electrons from the atoms in your hair get transferred to the balloon.0313

                                  The balloon now has a net negative charge and your hair, because it lost some electrons, now has a net positive charge.0317

                                  You can also charge conductors by contact.0324

                                  For example, if you bring a charge conductor into contact with an identical neutral conductor, you will share the charge across those two conductors.0327

                                  Let us take a look and see how that would work.0335

                                  A conductor carrying a net charge of 8 elementary charges is brought into contact with an identical conductor with no net charge.0338

                                  When they are brought into contact because their conductors and charges can move freely, those charges -- those 8e -- they are all positive; that is a positive charge; they are going to repel; they want to get as far apart from each other as they can.0346

                                  So what do they do? They split up so you get 4e on each conductor.0357

                                  If those conductors are identical, then you get the exact same charge on each.0361

                                  Then if you split them apart, you now have 4 elementary charges on each object.0365

                                  So what would the charge be?0370

                                  4e on each one, is going to be 4 times the charge on an elementary charge -- 1.6 × 10-19 C, which is 6.4 × 10-19 C.0372

                                  Now on a conductor, the charge is always going to sit on the outside surface.0387

                                  So the electric field inside the conductor, as we talk about fields here soon, is always going to be 0.0392

                                  Something to remember is that an electric field inside a conductor is 0.0398

                                  Let us talk about the electroscope.0405

                                  The electroscope is a really cool tool that is used to detect small electric charges based on conduction.0407

                                  It consists of a conducting rod in a beaker that is then insulated from the outside world, except for this metal knob that sticks out the top.0413

                                  If you were to bring something like a positively charged rod over to it to share the charge, you are going to get a net positive charge on your metal rod and as that is distributed throughout the rod, at the bottom you have these two very thin leaves.0421

                                  If you have positive charges on each of the leaves, they are going to repel and you get a spreading of the leaves, which indicates that you have a charge.0434

                                  You could have the same basic thing happen if you were trying to do this with a negative charge.0442

                                  If we draw just the metal part of our electroscope here and we bring a negatively charged rod near it...0446

                                  ...well now the electrons that are already on that metal rod without even touching, they are going to be repelled from the negative charge there and they are going to try and hang out as far away as possible from that negative charge -- leaving this end positive.0456

                                  Well once again down here on those leaves you have negative charges on each leaves they will repel, so this is really a charge detector.0470

                                  You could also charge by induction -- that is charging a conductor without actually coming into contact with another charged object.0480

                                  So if we start off with a neutral electroscope here and bring a positive rod near it, we will have the electrons all want to gather near the positive charge -- opposites attract -- leaving a net positive charge down near the leaves of the electroscope; they will spread apart.0487

                                  Now what we are going to do though is while we hold that rod in place, we are going to connect this metal bar to ground and by some connection to ground -- to the earth through a conductor -- the earth acts as an infinite sync or source of electrons.0502

                                  If you need some electrons to balance things out you could pull them straight from the earth; we have tons of extras.0517

                                  If you need to get rid of some, you can throw them into the earth very easily.0522

                                  So now when you connect this to ground it sees all the positive charges here and you will start sucking some electrons up from the ground in order to make that balance nice and happy.0526

                                  Now if you disconnect the ground connection, those charges are stuck on the metal conductor, you have a net negative charge on the electroscope and of course down here where you once again have negative charges on the leaves, the light charges repel each other and you see the spreading of the scope.0535

                                  You have therefore charge to the electroscope by induction -- you have not touched it specifically to the source of charges to that glass rod.0553

                                  Let us talk about electrostatic attraction.0564

                                  A positively charged glass rod attracts object X. What can you say about the net charge of object X?0566

                                  Well before we can answer that, let us think about what could happen here.0574

                                  If we have a positively charged glass rod, it is pretty easy to see that if you have some other negatively charged object that it will attract.0577

                                  So without a doubt, you could say that you could attract a negatively charged object.0590

                                  That is easy, but what if the object is neutral?0594

                                  Well if it is a conductor and it is a neutral object, you will actually have some of the electrons in the object who will want to hang out over near the positive charge.0598

                                  It remains electrically neutral, but because you have a negative closer to the positive, then the positive-positive you have a net attractive force, so you can actually attract neutral objects.0607

                                  What on the other hand would happen if you had that positive rod and instead of a conducting sphere like we had there let us talk about an insulating sphere.0618

                                  Well the atoms actually in this insulating sphere are made up of a positive nucleus and a negative electron orbiting it or multiples.0629

                                  When you bring the positive charge near it, the electrons are going to want to be attracted to that positive rod.0642

                                  They will want to spend just a little bit more time in their orbits over toward that positive rod side.0647

                                  So you are going to actually get the atoms, polar atoms or molecules to polarize just a little bit the ones at the edge, and as they do that you have a slight attractive force that is stronger between the positive and negative than the repulsive force from the positive to the positive.0652

                                  You have created a slight polarization of those molecules electrically and you can attract a neutral insulator that way as well.0670

                                  So what is the answer?0679

                                  The net charge of object X could be neutral or it could be negative to get attracted.0680

                                  Same thing would happen if you have a negative glass rod, it could attract something that was either positive or neutral.0686

                                  The only way to prove that two objects are charged is by repulsion.0693

                                  You can attract neutral objects with one charged object; you cannot repel unless both objects are charged.0698

                                  Let us talk about Coulomb's Law as we try and quantify this electrical force of attraction or repulsion.0706

                                  As we know like charged objects repel and opposites attract.0712

                                  Charged objects therefore must apply a force upon each other -- that is known as the electrostatic force or the coulombic force.0717

                                  And similar to gravity, the force of attraction or repulsion is determined by the amount of charge instead of mass and the distance between the charges.0723

                                  So the electric force is equal to some constant (k) -- that is called the electrostatic constant, it has the value 9 × 109N-m2 per C2 × the charge on the first object × the charge on the second object divided by the square of the distance between them.0732

                                  It is another inverse square law -- and notice how similar that is to the force equation we had for gravity.0749

                                  Universal gravitational force was (g) -- m1m2/r2.0756

                                  Notice what we have here. Instead of (k), we had (g) for gravity and instead of charge we have masses and the distance between their centers.0765

                                  It is almost the same thing, just in a different regime.0777

                                  The biggest difference is that gravity cannot repel, while the electrostatic force can attract or repel.0781

                                  So determining the electrostatic force -- three protons are separated from a single electron by a distance of 1 micron or 1 × 10-6 m.0790

                                  Find the electrostatic force between them. Is that attractive or repulsive?0800

                                  Well let us answer the easy question first.0805

                                  If we have 3 protons, that is going to be a charge of +3 elementary charges, the electron will be -1 elementary charge, and opposite charges are going to attract.0807

                                  Now, however, let us find the force between them.0819

                                  Let us call our protons our first charge (q1), so that is going to be 3e or 3 × +1.6 × 10-19 C, which is 4.8 × 10-19 C.0823

                                  Our second charge (q2) is going to be -1 × our elementary charge (1.6 × 10-19 C) or -1.6 × 10-19 C.0836

                                  And the distance between them? R = 10-6 m.0850

                                  So now we can apply Coulomb's Law.0854

                                  The electric force = k (the electrostatic constant) times the product of our charges divided by the square of the distance between them.0857

                                  So that is going to be 9 × 109N-m2/C2 (k) × q1 (4.8 × 10-19 C) × q2 (1.6 × 10-19 C) all over the square of the distance between them -- 10-6 m2.0866

                                  Now I want you to notice something here -- I did not worry about the signs when I am using Coulomb's law.0889

                                  Although you can, it is usually a lot simpler to calculate the magnitude of the force and then use what you know about positive - negative charges, attraction or repulsion to figure out the direction of the force.0896

                                  Typically, do not worry about the signs of the charges.0908

                                  It is a lot easier to just figure it out using common sense once you have done your calculations.0911

                                  This implies then that the electric force, when I put all of this into my calculator, comes out to be right around 6.9 × 10-16 and the units of force of course are Newton's (N) and we already determined that that was an attractive force.0917

                                  Let us take a look at a deflecting electron beam.0937

                                  If we have a beam of electrons, a bunch of electrons all negative -- e-, e-, my symbol for electron (e-) -- all moving to the right.0940

                                  It is directed into the electric field between two oppositely charged parallel plates.0951

                                  What is the direction of the electrostatic force exerted on the electrons by the electric field?0956

                                  Well even though we have not talked about electric field formally yet, it is pretty easy to see what is going to happen to our electron beam.0960

                                  If these are negative charges, they are going to get attracted by this side so we are going to have a force that way to do attraction here, and they are going to be repelled by the negatives here so we will have a force that way.0967

                                  So our net force -- both of these are going up, it is going to deflect it up, so we have a net force upwards.0978

                                  Electric fields -- The electrostatic force, just like the gravitational force is a non-contact or field force -- we cannot see it.0989

                                  The way we can detect it is by placing a charge somewhere in space and then seeing what force it has acting upon it.0997

                                  The property of space that allows a charged object to feel a force is what we call the electric field -- that mental construct to help us understand what is going on.1005

                                  You detect the presence of an electric field by placing a positive test charge at various points in space and measuring the force the test charge feels.1012

                                  What that means is the electric field is always going to point in the direction of the force on a positive charge, not on a negative charge.1021

                                  The electric field points the direction of a force on a positive charge.1029

                                  We quantify this with the electric field strength vector (E) and that is the amount of electrostatic force observed by a charge per unit of charge.1034

                                  So the electric field strength (E) is the electric force divided by the amount of charge; it is the force per unit charge.1044

                                  Its units are going to be -- Well, force is Newton's (N), (q) charge is in coulombs so that is Newton's per coulomb (N/C) and we will later find out that that is equivalent to volts per meter.1052

                                  Newton's per coulomb or volts per meter is the same thing.1066

                                  And again, the direction of the electric field vector is in the direction a positive charge would feel a force.1070

                                  So let us take a look at another example -- finding the field between some metal plates.1078

                                  Two oppositely charged parallel metal plates at 1 cm apart exert a force of 3.6 × 10-15N on an electron placed between the plates.1083

                                  Calculate the magnitude of the electric field strength between the plates.1094

                                  Well let us write down what we know so far.1098

                                  First off, our parallel plates are 1 cm apart -- so the distance between our plates is 0.01 m and there is a force (an electric force) of 3.6 × 10-15N on an electron.1100

                                  What do we know about an electron?1115

                                  Its charge is -1e or -1.6 × 10-19C.1117

                                  We want the magnitude of the electric field strength, so we are looking for (E).1124

                                  Well from our definition, the electric field strength is the electric force divided by the charge, which is 3.6 × 10-15N/-1.6 × 10-19 C...1130

                                  ...which gives me an electric field strength of 2.25 × 104 N/C and that would be negative, but since it is asking us for the magnitude, our answer is just 2.25 × 104 N/C.1145

                                  Let us talk a little bit more about the electric field and how we might be able to visualize it.1167

                                  Since you cannot actually see it, you can visualize it by drawing what we call field lines that show the direction of the electric force on a positive test charge.1172

                                  The electric field lines always point away from positive charges and toward negative charges.1180

                                  Electric field lines never cross each other; they intersect conductors at right angles to the surface of the conductor; and stronger fields have closer or denser lines; and finally field's strength and line density decreases as you move away from the charges.1186

                                  So having giving you some of these basic rules for our electric field lines, let us take a look and see what they actually look like.1203

                                  Here I have four different examples.1209

                                  In the upper left I am showing a positive charge and the electric field lines radiating outward from that charge and because it is a positive charge, electric field lines go away from it.1212

                                  You have a radial pattern and here you have a more dense lines in closer to the charge, so you have a stronger electric field.1222

                                  The further away you get, you have less dense lines, you have a less strong electric field -- which we know of course because the electric field or electric force follows an inverse square law relationship.1231

                                  Around a negative charge, you also have this radial pattern but now the field lines point in.1245

                                  Lines point away from positive charges and end at negative charges.1251

                                  Now down here I have a couple of dipoles -- two charges near each other.1256

                                  If we find the electric field, what we are going to do is vector addition of the individual fields.1260

                                  But if you have a positive and a negative beside each other -- well electric field lines go from positive to negative charges.1266

                                  So we are going to get a pattern that looks kind of like this, and you could fill in more lines if you wanted to as you interpolate between them, and so on.1273

                                  The key is that they go from positive to negative -- they never cross -- and they show the direction of the force on a positive test charge.1284

                                  If I were to go take and put a positive charge right there in space, it is pretty easy to see that the net force it is going to feel is probably going to be somewhere in that direction.1291

                                  If I were to go take a positive charge and put it right there, that yellow positive charge is going to feel a force to the right -- toward that negative charge.1302

                                  The electric field line is telling you the direction of the force on a positive test charge.1309

                                  Now over here on the bottom right, we have two positive charges making a dipole.1316

                                  While electric field lines go away from positive charges and they do not cross, you end up with a pattern that looks kind of like this.1321

                                  What is interesting here is if you were to take a positive test charge and put it exactly in the middle of those two, the forces on it are going to balance out so you get a net force of 0.1327

                                  Right in the middle, you actually have a dead spot while you are exactly at that point.1340

                                  So that is a little help to get you going on visualizing electric field lines.1345

                                  Let us talk about calculating the electric field due to a point charge.1352

                                  Electric fields are caused by charges.1356

                                  The electric field due to a point charge can be derived from what we know about the electric field and Coulomb's Law.1358

                                  We already know that the electric field strength is the force divided by the charge and Coulomb's Law says that the electric force on two charged objects is this constant (k) times the product of the charges divided by the square of the distance between them.1363

                                  We can put those together to find a definition, or a formula for the electric field due to a point charge.1379

                                  If the electric field strength is force divided by charge and force is (k)q1q2/r2...1385

                                  ...and I still have this (q) in the denominator there, well we can cancel out or make a ratio of 1 from one of our sets of charges and we find that the electric field strength is kq/r2.1397

                                  That is the formula for the electric field due to a point charge.1412

                                  To find the electric field due to multiple point charges, take the vector sum of the electric fields due to each of the individual point charges-- you just keep adding them up in a vector fashion.1425

                                  So let us take a look at comparing electricity to gravity again, there are so many similarities.1436

                                  Force is F = (k)q1q2/r2 for electricity and for gravity it is (g)m1m2/r2.1442

                                  We have swapped the (k) for (g) and the (q) for (m), charge for mass, but the same basic pattern though.1449

                                  The field strength -- electric field strength is the electric force divided by the charge, the gravitational field strength (g) was the gravitational force divided by the mass -- again a nice parallel.1456

                                  The field strength due to a point charge was kq/r2 and for gravity that was gm/r2 -- the same parallel.1467

                                  Now they have different constants and notice (k) here on the left is 8.99 × 109?1477

                                  I tend to just make that a nice, simple 9 × 109, so if you see that written differently somewhere, do not worry, it is close enough.1482

                                  On the right side the gravitational constant is 6.67 × 10-11N-m2/kg2.1490

                                  Again, these are really just fudge factors to make the units work out and the charge units were coulombs; the mass units were kilograms -- a lot of parallels.1497

                                  Let us take a look at a little bit more in-depth problem solving.1508

                                  Find the electric field at the origin due to the 3 charges shown in the diagram.1513

                                  We have a +2 C charge here at (0,8), a +1 C charge here at (2,2) and a -2 C charge at (8,0).1517

                                  Well what we are going to do -- our strategy is going to be to find the electric field at the origin to each of the individual charges and then add those up in vector fashion.1527

                                  So let us start by looking at our green charge up here at (0,8).1536

                                  If that is a +2 charge the electric field is going to point away from it, so we are going to have the electric field going in all these directions and at the origin, that must be pointing down.1541

                                  So right away we know that we only have to worry about the (y) component.1551

                                  Now the electric field strength is kq/r2 where (k) is 9 × 109 and our (q) is 2 C and the distance from the origin to our charge is 8 m.1556

                                  So that is going to be 82 or 2.81 × 108 N/C down.1573

                                  And if I want to write that in bracket notation, my (x) component is 0 and my (y) component is going to be -2.81 × 108 N/C because we know that must be pointing down.1582

                                  So there is the electric field due to our green charge.1599

                                  Let us do the red charge next.1603

                                  The electric field due to that red charge is again kq/r2 where (k) is 9 × 109, (q) is -2C, but again we are not going to worry about signs at the moment -- let us get the magnitude and we will use common sense to figure out its direction...1605

                                  ...and its distance is 8 units from the origin, so 82 is going to give us the exact the same thing -- 2.81 × 108 N/C is the magnitude.1624

                                  But if this is a negative charge, electric field lines point in to negative charges.1634

                                  So from the origin, we must be going toward the right due to that -2 C charge, so this would be 2.81 × 108 N/C toward the right or in the positive (x) direction.1641

                                  In bracket notation, I am going to write that as 2.81 × 108 N/C and it has no (y) component.1653

                                  So we have the electric field due to the green charge, the electric field due to our red charge, so now let us see what it is due to our blue charge.1663

                                  If this is +1 C, it should be pretty obvious to see that the electric field at the origin will be pointing away from it -- that direction.1672

                                  So we will have components in the (-x) and the (-y) direction here.1679

                                  Let us find its magnitude -- E = kq/r2 which is 9 × 109, our charge is 1 C and now we have to get the distance from the origin to that charge.1684

                                  Well to do that, I am going to make a right triangle here and if that is 2 units and that is 2 units, then by the Pythagorean Theorem, this must be the square root of 22 + 22.1699

                                  So that is going to be over square root of 22 + 22 squared.1711

                                  Or 9 × 109/8, which is about 1.13 × 109 N/C, but that is going to be down and to the left at an angle of 45 degrees because it has equal (x) and (y) components, which we can see just from the symmetry of the situation.1719

                                  So that means that if I want to break this into (x) and (y) components, this is going to be equal to...1740

                                  ...Well we are going to have to have its magnitude 1.13 × 109 N/C and the (x) component, we will multiply by the cos(45 degrees) and I know that is going to be negative.1745

                                  And for the (y), it is also going to be -1.13 × 109 × the sin(45 degrees), the (y) component.1760

                                  And those are going to be the same -- sin(45) and cos(45) are the same thing.1770

                                  When I run that through my calculator, I find that that is going to be about -7.95 × 108 for the (x) and -7.95 × 108 for the (y) -- all in Newton's per coulomb.1774

                                  Now I want the total charge or the total electric field at the origin due to those three.1793

                                  So for the total, all I am going to do is I am going to add up the (x) components and add up the (y) components.1800

                                  My (x) components, I have 0 from the green charge, I have +2.81 × 108 from the red charge and I have -7.95 × 108 from my blue charge -- so that is the (x) component.1808

                                  For the (y) component, I have -2.81 × 108 (green) + 0 (red) - 7.95 × 108 (blue), and again all of that is N/C.1830

                                  So I will pull out my calculator and add up all my (x)'s and add up all my (y)'s and I end up with a total electric field of about -5.14 × 108 for the (x) and -1.08 × 109 for the (y) and all of that is in N/C.1850

                                  A little bit more math here to get through it but really the same basic concept -- find the electric field due to each of those points and then sum them up to get the total electric field over here at the origin.1874

                                  We have a component to the left, we have a component that is down so we are going to have something where we have a net electric field down in that sort of southwestern quadrant (Quadrant 3 of the graph).1888

                                  Let us take a look at another problem.1903

                                  Determine the (x) coordinate here on this line where the electric field is 0 using the diagram below.1906

                                  We have a +2 C charge here on the right and then +1 C charge here on the left.1912

                                  We are going to follow the same strategy again.1918

                                  Let us take a look at the electric field due to that blue charge and we will call that E1 and that will be kq1/r2.1921

                                  When we do this, let us try and figure out roughly where our answer is going to be.1933

                                  As I look down here, if I have a +1 C charge to the right, it is going to give me an electric field to the right; +2 C over here to the left is going to give me an electric field to the left.1938

                                  And because +2 is stronger, I would expect that my 0-point is probably going to be somewhere a little closer to the +1 charge than it is to the +2 charge.1948

                                  So I am going to make a guess and say that we are probably going to be somewhere over in that sort of region.1958

                                  If we call this distance between our +1 C charge there at -6 and our point (r), then that means that over here, this distance must be 11 - r.1965

                                  If I want to draw the electric field due to E2, due to this red charge, we will call that E2 is kq2 over -- and our distance now will be 11 - r2.1987

                                  We want to find out the point where those two -- where the net electric field is 0, so where those are going to be exactly equal in magnitude.2001

                                  Our total electric field is going to be -- well we have our blue electric field over here -- (k) × q1 (1 C) divided by r2 and we will have to subtract because this is going to the left -- the electric field due to the red charge.2011

                                  That will be -(k) and the charge is 2, divided by 11 - r2, and we want the point where that all is equal to 0.2036

                                  First thing I can do here as I look at my problem is I see a simplification right away -- we can divide (k) out of all of that.2049

                                  I could rewrite this then as 1/r2 and I will move the red part to the right-hand side, which is going to be equal to 2/(11 - r)2.2059

                                  Let us extend that out, that will be 121 - 11r - 11r = -22r + r2.2074

                                  Now with a little bit of math here, if I multiply both sides by r2, on the left-hand side I am going to get 1 = 2r2/121 - 22r + r2...2084

                                  ...or with some cross-multiplication -- 2r2 = 121 - 22r + r2.2100

                                  It is starting to look at a quadratic equation, so let us get it in that form.2110

                                  This implies then that 2r2 - r2 = r2 + 22r - 121 = 0.2115

                                  Now we can apply our quadratic formula.2126

                                  Some of you have calculators that may do that automatically or you can go through the work there and what I find is that I get a value for r of 4.56.2130

                                  It means if this is 4.56 then this distance, 11 - r, must be 11 - 4.56 = 6.44.2143

                                  So determine the x-coordinate where the electric field is 0 using the diagram below.2154

                                  If we want the x-coordinate, well now I just need to go back and finish this problem up.2160

                                  To get the x-coordinate, that is going to be -- well if we start here at -6 and we add this distance r to it (4.56), I get an x-coordinate of about -1.44.2165

                                  So it looks to me like our actual point for the correct answer should be at about -1.44 right about there and we will make our guesstimate go away.2179

                                  We have found the x-coordinate where the electric field is 0.2191

                                  Let us take a look at an example where we look at gravity and electricity.2199

                                  A distance of 1 m separates the centers of two small charged spheres.2203

                                  The spheres exert gravitational force (Fg) and electrostatic force (FE) on each other.2207

                                  If the distance between the sphere's center is increased to 3 m -- so we are tripling the distance -- the gravitational force and electrostatic force, respectively, may be represented as...2213

                                  This is an inverse square law problem again -- we have tripled the distance and because distance is squared, we are going to have a change by a factor of 9.2223

                                  Now is that going to be 9 times greater force or 1/9 the force?2233

                                  Well we are going to have a smaller force because they are getting further away.2237

                                  Because they are both inverse square laws, our correct answer must be A -- 1/9 the gravitational force and 1/9 the electrical force.2241

                                  We will have a last problem here.2254

                                  In the diagram below, (P) is a point near a sphere that has a charge of -2 C.2256

                                  What is the direction of the electric field at point (P)?2262

                                  The way I would start this sort of problem is if we have a negative charge, let us draw some electric field lines.2266

                                  Electric field lines point in to negative charges.2272

                                  This line is just going to keep going so it looks like over here at point (P), we would have an electric field pointing that direction.2277

                                  So the direction of the electric field at point (P) would be to the left as shown right there.2287

                                  Hopefully that gets you a good start on electric fields and forces.2297

                                  Thank you so much for your time. Look forward to talking to you soon.2300

                                  Make it a great day everyone!2303

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