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Lecture Comments (4)

1 answer

Last reply by: Kyle Kosic
Mon Apr 4, 2011 8:42 PM

Post by Kyle Kosic on April 4, 2011

When he has 1/a^2 * sin(theta), couldn't he replace sin(theta) with x/a?

0 answers

Post by Daniel Brook on February 21, 2011

The Y-component aspect of the continuous charge distribution at the perpendicular bisector was really hard to understand. All of the trigonometry became really confusing. Either a different method of solving would have been nice or a more in-depth explanation of the problem could have helped.

Electric Field of a Continuous Charge Distribution

  • We know that the E-field produced by a point charge q at a point P a distance r away is (kq/r^2)*r_hat, where r_hat is a unit vector along the direction from q to P. How can we use this knowledge to find the E-field for a charge distribution?
  • The answer is the following: Divide the charge into many, many small elements, each element being so small that it is essentially a point. Then, the E-field produced by each element dq is obtained by using the formula for the field of a point charge. The total E-field is obtained by adding all the fields produced by all the charge elements; in other words, the total E-field is the integral over the charge distribution of (kdq/r^2)*r_hat.
  • Examples are given that show how to calculate the E-field produced by a charged rod, a charged ring, and a charged disk. In all these cases, the main issue is to set up the integral correctly, beyond which it becomes a problem in the calculus of integrations. In setting up the integral, we exploit the symmetry of the charge distribution to simplify the integral expression.

Electric Field of a Continuous Charge Distribution

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.

  • Intro 0:00
  • General Expression For E 0:16
    • Magnitude of Electric Field
    • Disk: Spread Charge Distribution
    • Volume Contains Charges
  • Charged Rod One Dimension 16:28
    • Rod in X-Axis
    • Charge Density
    • Find Electric Field at Distance 'A'
  • Charged Rod, Cont. 32:48
    • Origin at Center, Extends From -L to +L
    • Dividing Rod into Pieces
    • Electric Field Produced At Point P
    • Another Element
    • 'Y' Components of Electric Field
  • Charged Ring 54:23
    • Find Electric Field Above the Center
  • Charged Disc 58:43
    • Collection of Rings
  • Example 1: Charged Disk
  • Example 2: Semicircle with Charge
  • Example 3: Charged Cylindrical Charge
Professor Jishi

Professor Jishi

Electric Field of a Continuous Charge Distribution

Slide Duration:

Table of Contents

Section 1: Electricity
Electric Force

56m 18s

Intro
0:00
Electric Charge
0:18
Matter Consists of Atom
1:01
Two Types of Particles: Protons & Neutrons
1:48
Object with Excess Electrons: Negatively Charged
7:58
Carbon Atom
8:30
Positively Charged Object
9:55
Electric Charge
10:07
Rubber Rod Rubs Against Fur (Negative Charge)
10:16
Glass Rod Rub Against Silk (Positive Charge)
11:48
Hanging Rubber Rod
12:44
Conductors and Insulators
16:00
Electrons Close to Nucleus
18:34
Conductors Have Mobile Charge
21:30
Insulators: No Moving Electrons
23:06
Copper Wire Connected to Excess Negative charge
23:22
Other End Connected to Excess Positive Charge
24:09
Charging a Metal Object
27:25
By Contact
28:05
Metal Sphere on an Insulating Stand
28:16
Charging by Induction
30:59
Negative Rubber Rod
31:26
Size of Atom
36:08
Extra Example 1: Three Metallic Objects
-1
Extra Example 2: Rubber Rod and Two Metal Spheres
-2
Coulomb's Law

1h 27m 18s

Intro
0:00
Coulomb's Law
0:59
Two Point Charges by Distance R
1:11
Permitivity of Free Space
5:28
Charges on the Vertices of a Triangle
8:00
3 Charges on Vertices of Right Triangle
8:29
Charge of 4, -5 and -2 micro-Coulombs
10:00
Force Acting on Each Charge
10:58
Charges on a Line
21:29
2 Charges on X-Axis
22:40
Where Should Q should be Placed, Net Force =0
23:23
Two Small Spheres Attached to String
31:08
Adding Some Charge
32:03
Equilibrium Net Force on Each Sphere = 0
33:38
Simple Harmonic Motion of Point Charge
37:40
Two Charges on Y-Axis
37:55
Charge is Attracted
39:52
Magnitude of Net Force on Q
42:23
Extra Example 1: Vertices of Triangle
-1
Extra Example 2: Tension in String
-2
Extra Example 3: Two Conducting Spheres
-3
Extra Example 4: Force on Charge
-4
Electric Field

1h 37m 24s

Intro
0:00
Definition of Electric Field
0:11
Q1 Produces Electric Field
3:23
Charges on a Conductor
4:26
Field of a Point Charge
13:10
Charge Point Between Two Fields
13:20
Electric Field E=kq/r2
14:29
Direction of the Charge Field
15:10
Positive Charge, Field is Radially Out
15:45
Field of a Collection of a Point Charge
19:40
Two Charges Q1,Q2
19:56
Q1 Positive, Electric Field is Radially Out
20:32
Q2 is Negative, Electric Field is Radially Inward
20:46
4 Charges are Equal
23:54
Parallel Plate Capacitor
25:42
Two Plates ,Separated by a Distance
26:44
Fringe Effect
30:26
E=Constant Between the Parallel Plate Capacitor
30:40
Electric Field Lines
35:16
Pictorial Representation of Electric Field
35:30
Electric Lines are Tangent to the Vector
35:57
Lines Start at Positive Charge, End on Negative Charge
41:24
Parallel Line Proportional to Charge
45:51
Lines Never Cross
46:00
Conductors and Shielding
49:33
Static Equilibrium
51:09
No Net Moment of Charge
53:09
Electric Field is Perpendicular to the Surface of Conductor
55:40
Extra Example 1: Plastic Sphere Between Capacitor
-1
Extra Example 2: Electron Between Capacitor
-2
Extra Example 3: Zero Electric Field
-3
Extra Example 4: Dimensional Analysis
-4
Electric Field of a Continuous Charge Distribution

1h 40m 12s

Intro
0:00
General Expression For E
0:16
Magnitude of Electric Field
1:29
Disk: Spread Charge Distribution
5:04
Volume Contains Charges
6:16
Charged Rod One Dimension
16:28
Rod in X-Axis
17:00
Charge Density
17:49
Find Electric Field at Distance 'A'
19:05
Charged Rod, Cont.
32:48
Origin at Center, Extends From -L to +L
33:11
Dividing Rod into Pieces
34:50
Electric Field Produced At Point P
35:09
Another Element
37:43
'Y' Components of Electric Field
42:15
Charged Ring
54:23
Find Electric Field Above the Center
54:48
Charged Disc
58:43
Collection of Rings
59:10
Example 1: Charged Disk
-1
Example 2: Semicircle with Charge
-2
Example 3: Charged Cylindrical Charge
-3
Gauss's Law

1h 27m

Intro
0:00
Electric Field Lines
0:11
Magnitude of Field
2:04
Unit Area and Unit Lines
2:59
Number of Lines Passing Through the Unit
6:45
Electic Flux: Constant E
6:51
Field Lines Equally Spaced
7:10
Area Perpendicular To Field Lines
7:46
Electric Flux
8:36
Area Perpendicular to Electric Lines
9:43
Tilt the Area
10:58
Flux of E Through Area
17:30
Electric Flux: General Case
20:46
Perpendicular at Different Directions
23:24
Electric Field Given On a Patch
27:10
Magnitude of Field
28:53
Direction is Outward Normal
29:34
Flux Through Patch
30:36
Example
36:09
Electric Field in Whole Space
37:16
Sphere of Radius 'r'
37:30
Flux Through Sphere
38:09
Gauss's Law: Charge Outside
46:02
Flux Through Radius Phase is Zero
50:09
Outward normal 'n'
54:55
Gauss's Law: Charge Enclosed
1:00:30
Drawing Cones
1:00:51
Example 1: Flux Through Square
-1
Example 2: Flux Through Cube
-2
Example 3: Flux Through Pyramid
-3
Application of Gauss's Law, Part 1

1h 6m 48s

Intro
0:00
When is Gauss Law Useful?
0:18
Need a Surface S
5:14
Gaussian Surface
5:50
Sphere of Charge
10:11
Charge Density is Uniform
10:30
Radius as 'A'
11:23
Case 1: R>A
11:58
Any Direction On Cone Is Same
20:28
Case 2: R<A
25:15
Point R Within the Surface
25:30
Concentric Cavity
31:11
Inside Circle and Outside Circle
31:48
R>A
32:17
R<B
36:40
Radius Dependent Charge Density
37:39
Sphere
38:09
Total Charge: Q
39:46
Spherical Shell
40:13
Finding Electric Field R>A
42:36
R<A
44:14
Example 1: Charged Sphere
-1
Example 2: Charged Spherical Cavity
-2
Application of Gauss's Law, Part 2

1h 19m 19s

Intro
0:00
Infinitely Long Line of Charge
0:13
All Points Same Magnitude
5:02
E is Perpendicular to Line
9:08
Gauss's Law Cannot be Applied to Finite Length
15:50
Infinitely Long Cylinder Of Charge
16:05
Draw a Cylinder of Radius 'R'
16:36
Line of Charge Along the Center
18:25
R<A
18:39
Electric Field of Special Direction
19:06
Infinite Sheet of Charge
25:12
Electric Field Above the Sheet
25:38
Point is Above Height, Cylinder Intersects
26:29
Curved Path
33:12
Parallel Plate Capacitors
37:16
Electric Field Between Sheets
39:16
Conductors
41:55
Adding Charge to Conductors
42:16
In Electrostatic Equilibrium Charges Stop Moving
44:37
Electric Field is Perpendicular to Surface
47:16
Excess Charge Must Reside on Surface
47:38
Example 1: Cylindrical Shell
-1
Example 2: Wire Surrounded by Shell
-2
Example 3: Sphere Surrounded by Spherical Shell
-3
Electric Potential, Part 1

1h 26m 57s

Intro
0:00
Potential Difference Between Two Points
0:16
Electric Field in Space By Stationary Charges
0:30
Point Charge Moves From A to B
1:37
Electric Field Exerts a Force
1:50
Electric Potential Energy
5:34
Work Done By External Agent
20:03
Change in Potential Energy is Equal to Amount of Work Done
24:06
Potential Difference in Uniform Electric Field
27:59
Constant Electric Field
28:22
Equipotential
40:22
Parallel Plates
40:52
Electric Field is Perpendicular to Plate
42:07
Charge Released at A from Rest
49:00
Motion of Charged Particle in a Uniform Electric Field
51:55
Example 1: Work by Moving Electrons
-1
Example 2: Block and Spring
-2
Example 3: Particle on String
-3
Electric Potential, Part 2

1h 31m 50s

Intro
0:00
Potential of a Point Charge
0:32
Potential Difference Between A to B
1:25
Draw a Circle
9:12
Tangential to Sphere
9:33
Moving Normally From Sphere
12:33
Potential Energy of a Collection of Charges
26:33
Potential Energy of Two Charges
26:44
Work Done in Assembling the Configuration
27:29
Bringing From Infinity to New Location
33:57
Work Done by External Agent
36:22
Potential Energy of the System
39:39
Potential Energy for Two Charges
40:00
Example
44:49
Two Charges
45:03
Speed at Infinity
48:01
Electric Field from the Potential
51:12
Finding E if V is Given
51:33
Electric Dipole
56:22
Two Equal and Opposite Charges Separated By a Distance
56:32
If a << r1 or r2
1:00:23
Example 1: Two Point Charges
-1
Example 2: Two Insulating Spheres
-2
Example 3: Electric Potential of Space
-3
Electric Potential, Part 3

1h 9m 12s

Intro
0:00
Continuous Charge Distribution
0:27
Finding Potential for a Charge Point
1:39
Potential Produced at P
4:42
Charged Ring
8:38
Electric Field at Some Point of Axis
9:13
Charged Disk
19:32
Collection of Ring
20:40
Finding Potential Point Above the Ring
22:19
Potential Due to The Ring
23:40
Finite Line of Charge
35:56
Line of Change Along the X-Axis and Y-axis
36:11
Example 1: Charged Rod
-1
Example 2: Bent Semicircle
-2
Example 3: Bent Semicircle with Variables
-3
Electric Potential, Part 4

1h 11m 16s

Intro
0:00
Charged Conductors
0:12
Adding Excess Charge to a Conductor
1:02
E=0 Inside Conductors
1:50
Excess Charges Must Reside on Surface
3:40
E Normal on the Surface
9:31
Surface of Conductor is Equipotential
11:59
Conducting Sphere
19:28
Adding Charge to the Sphere
19:41
Electric Field Outside is Concentrated at Center
20:05
Electric Potential is Same as Center
23:01
Example
26:24
Two Spheres with Distance and of Different Size
26:45
Connecting Both Spheres with Conducting Wire
27:22
Cavity Within a Conductor
39:43
Hollow Conductor
40:19
Electric Static Equilibrium
41:13
Electric Field is Zero Within Cavity
53:20
Example 1: Neutral Conducting Sphere
-1
Example 2: Conducting Sphere with Spherical Shell
-2
Capacitor

1h 24m 14s

Intro
0:00
Capacitance
0:09
Consider Two Conductor s
0:25
Electric Field Passing from Positive to Negative
1:19
Potential Difference
3:31
Defining Capacitance
3:51
Parallel Plate Capacitance
8:30
Two Metallic Plates of Area 'a' and Distance 'd'
8:46
Potential Difference between Plates
13:12
Capacitance with a Dielectric
22:14
Applying Electric Field to a Capacitor
22:44
Dielectric
30:32
Example
34:56
Empty Capacitor
35:12
Connecting Capacitor to a Battery
35:26
Inserting Dielectric Between Plates
39:02
Energy of a Charged Capacitor
43:01
Work Done in Moving a Charge, Difference in Potential
47:48
Example
54:10
Parallel Plate Capacitor
54:22
Connect and Disconnect the Battery
55:27
Calculating Q=cv
55:50
Withdraw Mica Sheet
56:49
Word Done in Withdrawing the Mica
1:00:23
Extra Example 1: Parallel Plate Capacitor
-1
Extra Example 2: Mica Dielectric
-2
Combination of Capacitors

1h 3m 23s

Intro
0:00
Parallel Combination
0:20
Two Capacitors in Parallel With a Battery
0:40
Electric Field is Outside
5:47
Point A is Directly Connected to Positive Terminal
7:57
Point B is Directly Connected to Negative Terminal
8:10
Voltage Across Capacitor
12:54
Energy Stored
14:52
Series Combination
17:58
Two Capacitors Connected End to End With a Battery
18:10
Equivalent Capacitor
25:20
A is Same Potential
26:59
C is Same Potential
27:06
Potential Difference Across First Capacitor (Va-Vb)
27:42
(Vb-Vc) is Potential Difference Across Second Capacitor
28:10
Energy Stored in C1,C2
29:53
Example
31:07
Two Capacitor in Series, 2 in Parallel, 3 in Parallel, 1 Capacitor Connected
31:28
Final Equivalent Circuit
37:31
Extra Example 1: Four Capacitors
-1
Extra Example 2: Circuit with Switches
-2
Calculating Capacitance

55m 14s

Intro
0:00
Considering a Sphere
0:28
Placing Charge on Sphere
2:14
On the Surface of Sphere
4:12
Spherical Capacitor
9:20
Sphere of Radius a and Shell of Radius b
9:40
Positive Charge on Outer Sphere
11:02
Negative Charge on Inner Sphere
11:26
Calculating Potential Difference
11:38
Parallel Plate Capacitor
22:38
Two Plates with Charges Positive and Negative
22:54
Separation of Plate
25:10
Cylindrical Capacitor
28:40
Inner Cylinder and Outer Cylindrical Shell
29:01
Linear Charge Density
30:41
Example 1: Parallel Plate Capacitor
-1
Example 2: Spherical Capacitor
-2
More on Filled Capacitors

1h 17m 13s

Intro
0:00
Electric Dipole is an Electric Field : Torque
0:13
Magnitude of Dipole
1:15
Starts to Rotate
5:38
Force qe to the Right
5:59
Finding the Torque
6:35
Electric Dipole is an Electric Field : Potential Energy
13:56
Electric Field Try's to Rotate
14:43
Object on Center of Earth
16:04
Applying Torque Equal and Opposite
17:05
Water Molecule
25:43
Carbon Molecules
31:39
Net Dipole Moment is Zero
32:11
Induced Dipole Moment
34:43
Filled Capacitor
35:27
Empty Capacitor with Charge on it
35:44
Inserting a Dielectric
36:08
Capacitor Partially Filled with Metallic Slab
44:33
Capacitor with Slab of Distance 'd'
44:54
Capacitor Partially Filled with a Dielectric Slab
51:59
Change in Potential Difference
53:28
Example 1: Parallel Plate Capacitor
-1
Example 2: Conducting Slab
-2
Electric Current

1h 19m 17s

Intro
0:00
Definition
0:20
Consider a Wire ,Cylindrical
0:40
Cross Sectional Area
1:06
Crossing Charges Will be Counted
2:50
Amount of Charge Crosses Cross Sectional Area
3:29
Current I=q/t
4:18
Charges Flowing in Opposite Direction
5:58
Current Density
6:19
Applying Electric Field
11:50
Current in a Wire
15:24
Wire With a Cross Section Area 'A'
15:33
Current Flowing to Right
18:57
How Much Charge Crosses Area 'A'
19:15
Drift Velocity
20:02
Carriers in Cylinder
22:40
Ohm's Law
24:58
Va-Vb = Electric Field times Length of Wire
28:27
Ohm's Law
28:54
Consider a Copper Wire of 1m , Cross Sectional Area 1cm/sq
34:24
Temperature Effect
37:07
Heating a Wire
37:05
Temperature Co-Efficient of Resistivity
39:57
Battery EMF
43:00
Connecting a Resistance to Battery
44:30
Potential Difference at Terminal of Battery
45:15
Power
53:30
Battery Connected with a Resistance
53:47
Work Done on Charge
56:55
Energy Lost Per Second
1:00:35
Extra Example 1: Current
-1
Extra Example 2: Water Heater
-2
Circuits

1h 34m 8s

Intro
0:00
Simple Rules
0:16
Resistance in Series
0:33
Current Passing Per Second is Equal
1:36
Potential Difference
3:10
Parallel Circuit, R1, R2
5:08
Battery, Current Starts From Positive Terminal to Negative Terminal
10:08
Series Combination of Resistances
13:06
R1, R2 Connected to Battery
13:35
Va-Vb=Ir1,Vb-Vc=Ir2
16:59
Three Resistance Connected in Series Req=r1+r2+r3
18:55
Parallel Combination of Resistance
19:28
R1 and R2 Combined Parallel
19:50
I=i1+i2 (Total Current)
24:26
Requ=I/E
24:51
A Simple Circuit
27:57
Current Splits
29:15
Total Resistance
31:52
Current I= 6/17.2
35:10
Another Simple Circuit
37:46
Battery has Small Internal Resistance
38:02
2 Ohms Internal Resistance, and Two Resistance in Parallel
38:24
Drawing Circuit
48:53
Finding Current
52:06
RC Circuit
55:17
Battery , Resistance and Capacitance Connected
55:30
Current is Function of Time
58:00
R, C are Time Constants
59:25
Extra Example 1: Resistor Current/Power
-1
Extra Example 2: Find Current
-2
Extra Example 3: Find Current
-3
Extra Example 4: Find Current
-4
Kirchhoff's Law

1h 42m 2s

Intro
0:00
First Kirchhoff Rule
0:19
Two Resistance Connected With a Battery
0:29
Many Resistance
1:40
Increase in Potential from A to B
4:46
Charge Flowing from Higher Potential to Lower Potential
5:13
Second Kirchhoff Rule
9:17
Current Entering
9:27
Total Current Arriving is Equal Current Leaving
13:20
Example
14:10
Battery 6 V, Resistance 20, 30 Ohms and Another Battery 4v
14:30
Current Entering I2+I3
21:18
Example 2
31:20
2 Loop circuit with 6v and 12 v and Resistance, Find Current in Each Resistance
32:29
Example 3
42:02
Battery and Resistance in Loops
42:23
Ammeters and Voltmeters
56:22
Measuring Current is Introducing an Ammeter
56:35
Connecting Voltmeter, High Resistance
57:31
Extra Example 1: Find Current
-1
Extra Example 2: Find Current
-2
Extra Example 3: Find Current
-3
RC Circuits

1h 20m 35s

Intro
0:00
Charging a Capacitor: Circuit Equation
0:09
Circuit with a Resistance , Capacitance and a Battery
0:20
Closing Switch at T=0
1:36
Applying Kirchhoff's Rule
6:26
Change in Potential is Zero
6:52
Solution Tau dq/dt= ec-q
16:25
Discharging a Capacitor
27:14
Charged Capacitor Connect to Switch and Resistance
27:30
Closing the Switch at T=0
28:11
Example
36:50
12V Battery with Switch and Resistance 10mili ohms and Capacitor Connected 10 Micro Farad
37:02
Time Constant
38:58
Charge at q=0 at t=1sec
40:16
Example
42:58
Switch With Capacitor and Resistance
43:31
What Time Charge C Has Initial Valve
45:17
How Long Charge Energy Stored in C to Drop Half of Initial Value
46:55
Example 1: RC Circuit 1
-1
Example 2: RC Circuit 2
-2
Example 3: RC Circuit 3
-3
Section 2: Magnetism
Magnetic Field

1h 38m 19s

Intro
0:00
Magnets
0:13
Compass Will Always Point North
3:49
Moving a Compass Needle
5:50
Force on a Charged Particles
10:37
Electric Field and Charge Particle Q
10:48
Charge is Positive Force
11:11
Charge Particle is At Rest
13:38
Taking a Charged Particle and Moving to Right
16:15
Using Right Hand Rule
23:37
C= Magnitude of A, B
26:30
Magnitude of C
26:55
Motion of Particle in Uniform Magnetic Field
33:30
Magnetic Field has Same Direction
34:02
Direction of Force
38:40
Work Done By Force=0
41:40
Force is Perpendicular With Velocity
42:00
Bending an Electron Beam
48:09
Heating a Filament
48:29
Kinetic Energy of Battery
51:54
Introducing Magnetic Field
52:10
Velocity Selector
53:45
Selecting Particles of Specific Velocity
54:00
Parallel Plate Capacitor
54:30
Magnetic Force
56:20
Magnitude of Force
56:45
Extra Example 1: Vectors
-1
Extra Example 2: Proton in Magnetic Field
-2
Extra Example 3: Proton Circular Path
-3
Magnetic Force on a Current Carrying Conductor

1h 4m 43s

Intro
0:00
Current Carrying Conductor in a Magnetic Field
0:19
Current Though the Wire Connected to Battery
1:22
Current Exerts Force Toward the Left
2:16
IF Current is Reversed ,Force Exerts on Right
2:47
Magnetic Force
3:31
Wire with Current 'I' and with magnetic Field
4:02
Force Exerted by Magnetic field
5:05
Applying right hand Rule
5:25
Let N be Number of Charge Carries Per /Vol
6:40
Force on Wire
8:30
Number of Charge Crossing in Time 't'
12:51
Example
22:32
Wire Bent to Semi Circle and Rest is Straight
22:51
Applying Constant Magnetic Field in 'y' Direction
23:24
Force n Straight Segment
23:50
Net Force
34:19
Example 1: Rod on Rails
-1
Example 2: Magnetic Force on Wire
-2
Torque on a Current Carrying Loop

1h 9m 6s

Intro
0:00
B-Field Parallel to Plane of the Loop
0:27
Loop in the X-Y Plane
1:06
Net Force on Loop
7:45
B-Field Not Parallel to Plane of the Loop
15:16
Loop in the X-Y Plane, Free to Rotate in X- Direction
15:32
Force on Out of Page and Force in to the Page
15:59
Loop Turns Through 90 Degrees
18:10
Magnetic Moment
36:26
Any Current Loop Has Current 'I'
36:51
Electric Dipole in Electric Field
38:17
Potential Energy
39:54
Magnetic Potential Energy of Dipole
41:05
Example
43:33
Circular of Radius 'r' With Magnetic Field and Pass Current
43:42
Torque
46:01
Example 1: Loop in Magnetic Field
-1
Example 2: Rotating Charge
-2
Magnetic Field Produced By Current, Part 1

57m 58s

Intro
0:00
Biot-Savart Law
0:11
Suppose A current Carrying Wire
0:50
Magnetic Field Produced by the Tiny Element is Also Tiny
3:09
Permeability of Free Space
4:56
B-Field of a Straight Wire
8:40
Wire in X Axis
9:05
What is the Magnetic Field Produce at Point p
9:16
Taking a Small Segment
9:57
If Length is Infinite
26:26
Semi Circular Wire
27:02
Semicircular Wire of Radius 'R'
27:22
Finding Magnetic Field at Center
27:48
Circular Current in Loop
33:37
Circular Loop with Current 'I'
33:47
Current Above the Center
34:00
Example 1: Loop Carrying Current
-1
Example 2: Concentric Loops
-2
Magnetic Field Produced By Current, Part 2

1h 19m 29s

Intro
0:00
Ampere's Law
0:16
Consider a Loop at Any Point in Loop
1:15
Long Cylindrical Wire
9:08
Wire of Radius 'r'
9:24
Magnetic Field is Tangent to Circle and Has Same Magnitude
10:15
B at r>R
21:58
B at r<R
23:08
B at r=R
25:49
Toroid
26:58
Wrap a Wire to Toroid
27:47
Calculating the Magnetic Field for 1 Loop
29:30
Solenoid
39:17
Coil With Many Turns
39:35
Each Loop Carrying Current
40:29
Taking Loop Within the Solenoid and Close the Loop
43:05
Applying Ampere's Law
43:33
Example 1: Infinitely Long Wire
-1
Example 2: Straight Wire
-2
Example 3: Two Parallel Conductors
-3
Example 4: Solenoid
-4
Magnetic Field Produced By Current, Part 3

50m 37s

Intro
0:00
Magnetic Force Between Parallel Conductors
0:16
Two Parallel Plate Capacitors with Current
0:40
Magnetic Field by i1
1:50
According to Right Hand Rule
2:37
Example
10:20
Wire of 4m Length
10:50
Mass of Wire 1Kg
11:18
Force of Repulsion =Mg
12:24
Gauss's Law in Magnetism
15:36
Surface of Area, Magnetic Field is Perpendicular to Surface
17:09
Magnetic Flux Through Enclosed surface
19:23
Example
26:44
Magnetic Field Out of Page
27:54
Consider a Flux Through Rectangular Loop
28:52
Example 1: Two Parallel Wires
-1
Example 2: Cube with Magnetic Field
-2
Faraday's Law

1h 10m 38s

Intro
0:00
Faraday's Law
0:14
Coil Connected to Ammeter
0:29
Introducing a Magnet
1:08
Moving the Magnet Forward and Backward
1:33
Flux Increasing in Time
2:20
Induced Electro Motive Force EMF
4:20
Iron Core Square with Battery and Switch, Ammeter
5:22
Close the Switch, Current Appears
6:11
Lenz's Law
9:17
Wire with Current I and Wire Loop
9:30
Magnetic Field is Into the Page
10:14
Current Induced in Wire to Oppose Change in Flux
12:54
Example: Two Wires with Resistance and Uniform Magnetic Field
16:00
Increasing B
29:02
Coil of 100 Turns
29:20
B Perpendicular to Coil
30:47
Flux Through Each Turn
32:25
Rotating Coil
37:36
Consider a Big Magnet and Rectangular Coil with many Turns
37:49
Rotating Coil With Angular Velocity 'w'
41:49
Example 1: Loop
-1
Example 2: Solenoid
-2
Example 3: Wrapped Square
-3
Motional EMF

1h 17s

Intro
0:00
Moving a Conducting Rod in Magnetic Field
0:24
Rod Moving in a Plane with Velocity 'v'
0:49
Charges Piles Up and Down Until Electric Force Balance 'B'
7:59
Equilibrium
9:30
Potential Difference, Distance to Length of Wire
9:59
Rod Pulled By External Agent
11:30
Resistance to Wire
12:01
Introducing Uniform Magnetic Field into The page
12:14
Finding Flux
14:45
Power Delivered to Resistance
17:01
Force Exerted by 'B' on Rod
19:10
Power By Agent
22:26
Sliding Rod
23:08
Resistance with a Sliding Rod and Magnetic Field 'B'
23:35
Push With Initial Velocity 'V0'
24:01
Finding Current = I
25:20
Rotating Rod
36:10
Magnetic Field into The Page
36:19
Rod fixed in Plane and Rotating
36:40
Induced EMF in Segment
40:00
Example 1: Bar in Magnetic Field
-1
Example 2: Rod in Magnetic Field
-2
Induced Electric Field

1h 5m 19s

Intro
0:00
Change B to Induce E
0:54
Loop with Magnetic Field B
1:10
Flux is Positive With Choice of 'n'
2:45
Suppose Magnetic Field is Changing
3:04
B Changing with time Flux (>0)
3:24
Change in Electric Field Induces magnetic Field
20:34
Example
21:08
Cylinder with Magnetic Field
21:20
Fill With Radius 'r'
22:11
Turn Off the Field
22:30
Magnetic Flux Through Big Loop
29:59
AC Generator
38:28
Magnetic Field with Coil of Many Turns
38:50
As the Coil Rotates Flux is Induced
39:18
Coil Rotated by Angle
40:29
Coil Connected to The Ring and End Connected to Lamp
42:12
Kinetic Energy Strike the Coil and Rotating Coil will Produce Electric Energy
45:12
Example 1: Electric Field
-1
Example 2: Electric Field
-2
Inductance

1h 11m 10s

Intro
0:00
Mutual Inductance
0:10
Two Coils
0:35
Current is Time Dependent
0:54
Flux Proportional
1:55
Magnetic Flux in Coil 2
2:08
Induced EMF
2:40
Flux Through 2nd Coil Proportional to Current in First Coil
4:07
Mutual Inductance
5:30
Suppose Current is in 2nd Coil
9:28
Example
12:15
Two Coils M=0.001
12:26
Φ= Mi1
14:17
Induced EMF
15:44
Example
18:30
Solenoid with N turns
18:40
B inside Solenoid
21:05
Φ Through the Ring
22:14
Self Inductance
27:50
Single Coil with Current
28:33
I with Time Dependent
28:54
Φ Proportional to B , Proportional to I
30:00
Induced EMF =-di/dt
31:27
Example 1: Circular Wire
-1
Example 2: Two Coils
-2
Example 3: Coil
-3
RL Circuits

1h 25m 19s

Intro
0:00
Current Raising
0:45
Battery and Switch with Resistance and Inductance
1:17
Close s1 at T=0
2:27
With out Inductor , Current is E/R
4:03
I at T=0
9:51
Vb-Va= -Ir
15:05
Log (i-e/r)
19:51
Current Declining
27:16
Resistance R and Inductance
27:37
I= E/R
28:37
Switch is On at T=0
29:10
Example
39:46
Battery and Resistance R Connected with Inductor
39:55
Time Constant l/R
40:58
Time to Reach Half Time
41:59
per τ (1-1/e)
44:36
Magnetic Energy
45:47
E-IR-Ldi/dt
46:26
Power Derived By Current
46:51
Magnetic Energy Stored in Conductor
52:48
U=Li2
55:28
Magnetic Energy Density
57:49
Solenoid
58:18
U=1/2 Li2
59:03
Energy Density
1:00:45
Example 1: Circuit 1
-1
Example 2: Circuit 2
-2
Circuit Oscillation

1h 22m 26s

Intro
0:00
Oscillation in LC Circuit: Qualitative Analysis
0:30
Circuit with Capacitance and Inductance
1:27
Comparison with a Spring Block System
4:57
Close the Switch, Let the Block Move
5:51
At V=0
7:06
LC Circuit Oscillation :Quantitative Analysis
15:07
U Total = Ue + U m
17:26
Example RLC
29:25
Battery =12V, Capacitor and Inductor
29:54
Switch at B F> t
31:42
Damped Oscillation
50:14
Example 1: LC Circuit 1
-1
Example 2: LC Circuit 2
-2
Example 3: RLC Circuit
-3
Maxwell's Equations

1h 12m 35s

Intro
0:00
Displacement Current
1:29
Ampere's Law
3:04
Surface Bounded by Path
3:48
I Current Going Through Surface
4:53
Charging a Capacitor
9:55
Maxwell's Equation
18:26
Integral Form
18:53
E.da =Q/e0 in Closed Surface
18:55
Absence of Magnetic Monopoles
19:55
Flux Through the Surface Bounded By C
22:26
Ampere's Law
23:01
Plane Electromagnetic Wave
31:03
Electric and Magnetic Field
31:27
Example
39:20
Electromagnetic Wave Traveling in X Direction
39:40
Lamda=c/f
41:30
B=E/C
43:49
Energy and Momentum Carried by EM Waves
44:34
Energy Density
46:35
Area in Y-Z Plane , Wave in X -Direction
48:53
Energy Crossing Per Unit Area
52:53
Pointing Vector
53:11
Reflection of Radioactive
1:00:26
Example 1: Cylindrical Region
-1
Example 2: Electric Field of EM Wave
-2
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