AP Physics 1 & 2 Magnetic Fields & Properties

Hi everyone. I am Dan Fullerton and I would like to welcome you back to Educator.com.0000

This lesson is on magnetic fields and properties.0004

Our objectives are going to explain that magnetism is caused by moving electrical charges, describing the magnetic poles and interactions between magnets, drawing magnetic field lines, recognizing magnetic permeability (magnetic dipole moment) as properties of matter...0007

...calculating the force exerted on a charge moving through a magnetic field and explaining the operation of a mass spectrometer.0023

Let us start by talking about what magnetism is. Magnetism is a force caused by moving charges.0031

Magnets are dipoles; they all have a north and a south. You cannot have a north without a south or a south without a north and there are no magnetic monopoles.0038

Like poles repel and opposite poles attract.0047

Now magnetic domains are clusters of atoms with electrons spinning in the same direction.0051

Atoms have those moving electrons, therefore they are magnetic, so the same thing here as we have magnetic domains -- electrons spinning in the same direction and we get a net that we call magnetic domain.0056

If we have random domains where they are all pointing in random directions, you do not have any net magnetic field, but if you can get some of those domains to point in the same direction, you could end up creating a strong magnet because you have a net magnetic field all pointing in the same direction.0066

To start off with -- Which type of field is present near a moving electric charge?0083

Not an electric field only because a moving charge has a magnetic field and not a magnetic field only because you still have the electric field.0089

So what type of field is present? You must have both an electric field and a magnetic field.0097

You have the electric field because you have a charge and because it is a moving charge, you get a magnetic field.0102

Now magnetic field strength is a vector quantity. It is given the symbol (B), typically, and its units are teslas (T), where 1 T is equal to 1 Newton second/coulomb meter.0109

Now magnets are polarized; each has two opposite ends. You have a north with a south.0125

The end of the magnet that points toward the geographic North Pole of the earth is called the North Pole of the magnet.0130

Now there are no magnetic monopoles again; you cannot have a north without a south or a south without a north.0137

Magnetic field lines make closed loops and run from north to south outside the magnet.0145

Very similar to electric field lines, magnetic field lines run from North to South and they continue through the magnet, but outside the magnet, they always run from North to South.0150

Now the density of the magnetic field is known as the magnetic flux, so you have more magnetic flux in a region like this than you do in a region like this because the magnetic field lines are closer.0160

The magnetic field lines show the direction the North Pole of a magnet would tend to point if it were placed in that field.0172

Now because we are going to have to deal with three dimensions as we answer some of these problems and analyze some of these situations, we need a way of representing that on a page that is only two-dimensional.0180

Up, down, left and right on a page are pretty easy, but how about if you want to go out of the page.0190

Well, to represent a vector pointing out of the page or toward you out of the screen, you would put a dot or sometimes you will see it as a dot with a circle around it.0196

Imagine that is an arrow. If the point is coming toward you, what you are going to see is the point, so it is coming toward you or out of that plane.0205

If it was going away or into that plane, you would see the fletching's on the arrow, so those are typically shown as x's or x's with a circle around them.0213

That would be pointing into the plane here or going into your screens at home.0222

Let us take a look at another example where we have lines of magnetic force.0231

The diagram below shows the lines of magnetic force between two North Magnetic Poles.0234

At which point is the magnetic field strength greatest?0240

That is going to be where we have the densest lines or over here at B -- densest lines -- therefore you have the greatest magnetic flux.0244

The density of the magnetic field, our B field is known as magnetic flux and it gets the symbol Φ, magnetic flux.0253

Sometimes you will see that written as Φ_B to show that it is magnetic or even as Φ_M for magnetic.0272

Let us take a look at an example where we look at forces between bar magnets.0281

The diagram below represents a 0.5 kg bar magnet and a 0.7 kg bar magnet with a distance of 0.2 m between their centers.0284

Which statement best describes the forces between the bar magnets?0293

The gravitational force and magnetic force are repulsive.0296

Well, if we have like poles, they are going to repel, so the magnetic force is going to repel, but gravity can never repel; gravity can only attract, so it cannot be A.0300

Gravitational force is repulsive. No, gravity still cannot repel.0311

Gravitational force is attractive. Yes, that looks good.0315

Magnetic force is repulsive. Now, that has to be it because we have two North's, so they will repel magnetically and the gravitational force will attract.0318

Let us take a look at the compass. The earth is a giant magnet.0328

The Earth's magnetic north pole is located near the geographic S pole of the earth and vice versa.0333

The reason that is is if you were to take a magnet and you want to put it somewhere on Earth, you want the north end of the magnet, of the compass to point toward the N magnetic pole.0339

If this is the north end of the compass, it is going to be attracted to the magnetic south at that part of the earth.0349

So the geographic N pole is Earth's magnetic south and the geographic S pole, where the penguins live, is the magnetic north pole of the earth, and the compass lines up with a net magnetic field.0356

Now having talked about magnetic north and magnetic south poles, somewhat interesting, in actuality, the magnetic north and south pole of the earth are constantly moving.0370

The current rate of change of the magnetic north pole is thought to be somewhere around 20 km per year or even perhaps more than that.0379

It is believed that it has shifted more than 1,000 km since it was first reached by an explorer in 1831.0387

That is a lot of movement for what we base all of our compasses on.0395

Let us take a look at a problem with a compass and a magnetic field.0401

The diagram below represents the magnetic field near point (P).0405

If a compass is placed at point (P) in the same plane as the magnetic field, which arrow represents the direction of the north end that the compass needle will point?0408

If we were to put a compass here at point (P), compasses line up with the magnetic field, so it would point in the same direction.0417

Our compass arrow would look kind of like that -- pointing in the same direction.0424

Compasses line up with the net magnetic field.0430

The diagram below shows a bar magnet.0435

Which way will the needle of a compass placed at a point?0438

Well, let us draw the magnetic field lines; they run outside the compass from north to south and a compass lines up with a magnetic field.0440

If that was our compass -- I will draw it here in purple -- it would be pointing that direction, toward the right, which makes sense because the north end of a compass is attracted to the south end of the magnet and the south end of the compass is attracted to the north end of the magnet.0459

That should make sense there, so it would point to the right.0475

Now magnetic permeability, a fancy term that refers to the ratio of the magnetic field strength induced in a material to the magnetic field strength of the inducing field or kind of how susceptible a material is to magnetic fields.0480

Free space vacuum has a constant value of magnetic permeability that appears in physical relationships.0493

That is called the permeability of free space and it is 4π × 10^-7 tesla meters/amps.0499

The permeability of matter has a value different from that of free space.0509

Highly magnetic material such as iron have higher values of magnetic permeability.0513

Another term we are going to have to know is magnetic dipole moment, which is also sometimes called just the magnetic moment.0520

The magnetic dipole moment of a magnet refers to the force the magnet can exert on moving charges.0526

In simplistic terms, you can think of that as the relative strength of a magnet, so the magnetic dipole moment of a hydrogen atom compared to the magnetic dipole moment of a highly magnetized iron bar -- well, the magnetic dipole moment of the iron bar is certainly going to be a whole lot stronger.0532

We know moving charges create magnetic fields, but does it work the other way?0550

Well, yes. Magnetic fields exert forces on moving charges and we can find the magnitude of that magnetic force (F_B) is equal to the charge times the velocity of your charged particle times the magnetic field strength (B) times the sine of the angle between the velocity of the moving charge and the magnetic field direction.0555

The magnetic force is measured in Newton's, the charge is measured in coulombs, velocity is measured in m/s, magnetic field strength in tesla, and the angle between them should be a θ, the angle between the velocity vector and the direction of the magnetic field.0578

Now the direction of the magnetic force -- this is going to take little bit more work.0597

We found the magnitude pretty easily using that formula.0602

The direction of the force is given by the right-hand rule.0604

Here is how that works. Point the fingers of your right hand in the direction of the positive particles velocity.0607

If it is a positive particle, use your right hand to point your fingers in the direction of its velocity.0615

If it is moving this way, your fingers are going in that direction.0619

Then bend your fingers inward in the direction of the magnetic field.0622

Let us assume we have a particle going this way and a magnetic field pointing right toward me, so I would point my finger in the direction of the particle's velocity, bend them toward the magnetic field and my thumb is going to point in the direction of the magnetic force.0627

That is called the right-hand rule.0642

If you have a negative charge or it is an electron that is moving, go ahead and use your left hand, but the same rules.0644

A mass spectrometer is used to determine the mass of an unknown particle.0653

Because magnetic fields accelerate moving charges, so that they travel in a circle, this can be used to determine the mass of an unknown particle.0658

Here is the idea. If we put an unknown charged particle into this magnetic field -- a uniformed magnetic field of strength (B -- we can figure out where it lands here and measure the radius.0665

Knowing the radius and a few other things, we can figure out what the mass of that particle must be.0676

Let us take a look and analyze it from the perspective of circular motion because it is moving in part of a circle here.0682

In order to move in a circle, it must have a centripetal force, which we know is mv²/r from our mechanic's days, but what is causing that centripetal force?0690

Well, that is the magnetic force and we know the magnitude of that is qvBsin(θ).0700

In this case the force is always going to act at an angle of 90 degrees to the velocity.0709

The magnetic field is acting at an angle of 90 degrees to the velocity, so the sin(θ), θ is going to be 90 degrees, so sin(90 degrees) = 1, so mv²/r = qvB.0716

Some simplifications we can make here is we can divide a (v) out of both sides and I can rearrange this then to say that mass must equal qrB divided by the particles velocity.0735

To know the charge on it, find the radius by measuring where it hits here, given the known magnetic field strength and the known incoming velocity, you can figure out the mass of that unknown particle.0751

A velocity selector works on a similar principle; it is a mass spectrometer, but you add an electric field.0764

Now, the electric force down has to balance the magnetic force up.0770

So, here is the idea -- If we have a charged particle coming in here, we have a uniformed magnetic field.0774

That is going to want to cause our particle to go this way, to go up and make that circular path.0780

But if we apply an electric field as well, the electric field in this direction is going to offset that, so we want the electric force to balance the magnetic force in order for that particle to go directly through our velocity selector.0787

If that is going to happen, the electric force must be equal in magnitude to the magnetic force or we know that the electric force is charge times the electric field and the magnetic force is qvB and we already talked about the angle being 90 degrees, so the sin(θ) does not really play in here because that is 1.0801

We can divide the charge out of both sides and then see that the velocity that allows a particle to go directly through here is just the electric field strength divided by the magnetic field strength.0821

So if we tailor our electric field strength and magnetic field strength just right, only particles at the specific velocity we want will make it directly through here.0834

Everything else is either going to be deflected one way or the other.0840

Let us look at the force on an electron.0853

An electron moves at 2 × 10⁶ m/s -- V = 2 × 10^-6 m/s -- and it is an electron so we know its charge is -1.6 × 10^-19 C perpendicular (θ = 90 degrees) to a magnetic field having a flux density of 2 T, so our magnetic field strength, the flux density is 2 T.0856

What is the magnitude of the magnetic force on the electron?0881

The magnetic force, F_B = qvBsin(θ), which is going to be (q) -1.6 × 10^-19 C, our velocity (2 × 10^-6 m/s)...0885

...our magnetic field strength (2 T) × sin(90 degrees).0904

If I put all of that into my calculator, I find the magnetic force is 6.4 × 10^-13 N.0911

How about the velocity of a charged particle?0925

A particle with a charge of 6.4 × 10^-19 C experiences a force of 2 × 10^-12 N.0928

As it travels through a 3 T magnetic field at an angle of 30 degrees to the field, what is the particle's velocity?0942

We will go back to our formula for the magnitude of the magnetic force, F_B = qvBsin(θ).0954

Therefore velocity is going to be equal to the magnetic force divided by qBsin(θ)...0969

...or V = 2 × 10^-12 N/6.4 × 10^-19 C (charge) × 3 T (magnetic field strength) × sin(30 degrees).0981

When I put all of that into my calculator, I come up with a velocity of about 2.08 × 10⁶ m/s.0999

How about a right-hand rule problem?1012

The diagram shows a proton, a positive charge moving with velocity (V) about to enter a uniformed magnetic field directed into the page.1015

As the proton moves in the magnetic field, determine the direction of the force on the proton.1022

First thing you are going to do is take your right hand, since it is a positive charge and point the fingers of your right hand in the direction of the velocity.1027

Now the magnetic field is (x), so that is directed into the page, so bend your fingers 90 degrees into the page.1035

Your thumb points in the direction of the magnetic force, and in this case if our particle is moving to the right, our fingers point in that direction, they bend into the page and we will find that our thumb should point up, the direction of the force on the particle.1045

For each diagram below, indicate the direction of the magnetic force on the charged particle.1064

Well, the first thing we need to do over here on the left is realize that the magnetic field runs from North to South outside the magnet, so our magnetic field is going to look like it has that direction.1069

Then we are going to take our left hand because it is a negative charge and point the fingers of your left hand in the direction of the particles velocity, bend them down in the direction of the magnetic field and you should find that your thumb is going to point into the plane of screen.1082

Therefore the direction of the magnetic force in this case is going to be into the plane that way.1097

Over here on the right hand side, we have a positive charge, so we can use our right hand.1106

Point your right hand in the direction of the particle's velocity, bend your fingers in the direction of the magnetic field into the plane and you should see that your thumb points toward the left of the screen, so you would get a magnetic force in this case to the left.1110

Just practicing using those right-hand rules or left-hand rules if it is a negative charge.1126

Last question -- An electron released from rest in a magnetic field.1134

An electron is released from rest between the poles of two bar magnets in a region where the magnitude of the magnetic field strength is 6 T, as shown below.1139

What is the magnetic force on the electron?1149

Here is the key. It is at rest, so the magnetic force is going to be 0, since V = 0.1152

Remember F_B = qvBsin(θ). You only have that force on a moving charge.1163

If V = 0, then that whole thing is 0; no magnetic force, so our answer is 0.1171

Hopefully that gets you a good start on magnetic fields and magnetic properties.1180

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