AP Physics 1 & 2 Intro to Electromagnetic Induction

Hi everyone. Thrilled to have you back with us at Educator.com.0000

This lesson is going to be an introduction to electromagnetic induction.0003

Our objectives are going to be explaining how a changing magnetic flux through a loop of wire can create an induced electromagnetic force, or an induced potential difference; calculate the magnetic flux through a loop of wire, calculate the induced EMF using Faraday's Law...0009

...find the induced EMF in an expanding or contracting rectangular loop of wire, utilize Lenz's Law to determine the direction of the induced current flow, and finally explain the basic operation of an electric generator or motor, something we touched on last time.0025

Induced EMF or electric motor force -- Charges flowing through a wire create magnetic fields.0041

Now, changing magnetic fields can cause charges to flow.0049

They induce a current in the process known as electromagnetic induction.0052

The potential difference created that causes that current to flow by that changing magnetic field is known as the induced EMF or electromotive force.0057

Now do not get fooled here. Even though it says electromotive force, it is not really a force.0065

It is a potential difference or a source of potential difference that causes current to flow.0071

The amount of magnetic field passing through an area is known as the magnetic flux, and that is given the Greek symbol φ often times you will see that written as φB for magnetic or φM.0076

The units of magnetic flux are webers (Wb), where one weber is equal to 1 Tm².0087

Finding the magnetic flux -- the magnetic flux through a given area (A) due to some magnetic field (B) can be determined as the flux is equal to the magnetic field strength times the area times the cosine of the angle between (B) and (A)...0096

...where when we talk about the angle of (A), we are talking about a vector that is perpendicular to that area.0111

As an example down here, if (B) is the magnetic field strength, (A) is the area through which the flux must pass, then θ is the angle between them.0119

Here we are showing all of the flux passing through the area; they are perpendicular, so φ, our flux would be BA, almost like you have your hand here and you are blowing directly into it.0127

The flux, the magnetic field, the wind is all hitting that in passing through it.0140

Over here, however, we have now turned that area, so it is going sideways as if you are blowing across your hand.0145

You are not getting nearly the amount of flux, nearly the amount of wind through it; it is all going around it.0153

Over here, because our angle would be 90 degrees, we have φ = 0, where the direction for the angle -- there is the direction of (A), so that would be 90 degrees or the area compared to that over here where they are in the same direction with no flux.0159

I think that is clear without me making that any worse.0177

Calculating the induced electromotive force -- The magnitude of the induced EMF is equal to the rate of change of the magnetic flux.0182

The area can change, the magnetic field strength can change, or the angle could change.0189

So the average induced EMF -- written this way with that epsilon -- is equal to the opposite of the change in magnetic flux divided by time.0195

That negative sign just has to do with the direction of the induced current.0204

We figure this out typically -- instead of worrying about it in the formula, we will use Lenz's Law to help us figure out that direction, which we will talk about very shortly.0209

Now if the flux passes through multiple loops of wire, all you do is you multiply the flux by the total number of loops you have.0219

So if there are multiple loops, then you could say that the average EMF is going to be equal to minus and the number of loops times your change in the magnetic flux divided by the interval of time.0225

Let us take a look at induced EMF in a rectangular loop of wire.0243

The induced EMF -- let us find its magnitude -- is equal to the change in the magnetic flux divided by that time interval.0248

Well, that magnetic flux, that is just going to be change in (BA), the magnetic field strength times the area there divided by that time interval.0256

But if this is a constant magnetic field strength, that is B(δ)A/δT, but the area is going to be this length times that x-dimension, so that is going to be δLx/δT.0267

But again in this diagram, (L) is not changing, it is a constant, so we can pull that out of the delta and we get BL(δ)x/δT.0288

What is δx/δT?0299

Well that is velocity, so that is just BLV, the induced EMF due to a rectangular loop of wire expanding with some velocity.0302

Now Lenz's Law is probably the toughest part of electromagnetic induction, but once you understand it, it is so simple.0318

What it states in words is the direction of the induced current always opposes the change in flux.0326

Putting it in words makes it so much more complicated than just doing it and trying to understand what is going on.0332

Here we have a magnet and we are going to put it through a loop of wire and let us assume that our magnet, we are moving it downwards.0338

While the flux from our magnet -- remember the magnetic field is going to run from North to South, so coming out of North, we have our flux going that direction and as it gets closer and closer, what is going to happen due to the magnet moving this way?0347

Well we are going to have more flux going down through that hoop, so pushing this down is going to put more flux through that hoop.0361

The current wants to oppose any change in flux through the loop, so if we are putting more through here by moving this down, the induced current wants to go the opposite direction, so we are going to think of this as if we are trying to put some flux the other direction.0369

Now we can use our right-hand rule and say well, if we have magnetic flux going that direction, through the loop, wrap the fingers of our right hand in that direction and that would only occur if we had current flowing in that direction in the wire.0386

Pushing the magnet down creates more flux down through and we want to oppose that change, so we will have flux going the opposite direction and then figure out, using the right-hand rule, the direction of the current using that opposing magnetic flux because the direction of induced current always opposes any change in flux.0402

Let us take a look down here at this example.0422

We are going to do the same basic idea, but now we are going to move our magnet this way.0424

Once again, the magnetic flux was going this way down through the loop, but as we pull the magnet away as we move it up away from that loop, we are going to have less magnetic flux going down through there.0429

Well, the induced current wants to oppose that, so if we have less going down, it is going to want to oppose it by having more flux going down.0441

Now we can use our right-hand rule again -- point our thumb of our right hand in the direction of that magnetic flux that is opposing and we would get a current flow by the right-hand rule that is now in this direction using Lenz's Law to determine the direction of the induced current.0449

Now let us flip the magnet around and see what happens.0468

Over here on the right, the upper right, let us assume that we are pushing the magnet down through that loop again, but now do we know magnetic field lines run into the South.0471

As we are pushing this down in through that loop, what we are actually doing is we are creating more magnetic flux and it is pointing in this direction, so we want to oppose the magnetic flux in that direction.0483

As I point my finger in the direction of the opposing magnetic flux, using the right-hand rule, I can determine that the current should be moving that way around the loop.0497

Finally, the last situation we will assume we are pulling the magnet up out of that loop.0509

Again, the field lines go into the South -- so as that is going up this way, we are reducing the magnetic field going through this direction, and we are going to have induced magnetic field that wants to keep that going that way.0514

We want to continue in the state that it was and if we are having less going up, the induced current is going to want to put more going up, so it stays in the same state.0532

Now we can use our right-hand rule again -- point the thumb of our right hand in the direction of that opposing magnetic flux and I would get then a current that is flowing in roughly that direction.0541

That is Lenz's Law; it takes a little bit of practice, a little bit of doing, but it is a lot easier than chasing down those negative signs.0558

Electric generators and motors -- By turning a coil of wire in a magnetic field, you can generate an induced EMF because you are changing the flux through that loop.0568

Generators use mechanical energy of some sort to turn the coil of wire or to turn a magnet inside a coil of wire to create a change in magnetic flux and therefore create a source of potential difference.0579

Think of hydroelectric power where water moving spins either coils of wire or magnets around a coil of wire to change a magnetic flux, which is converted into an electric potential.0591

Or steam power that turns a fan and as that fan turns it is going to turn a coil of wire or a magnet to change a magnetic flux through a coil.0602

Nuclear power has the same idea where you use nuclear power to create a lot of heat, a lot of steam and that steam is then forced through fans which are then used in order to turn coils of wire or magnets, creating changing magnetic flux and therefore potential difference.0612

Very, very, very common.0628

Electric motors operate using the same basic principle and we talked about them a lesson or two ago, how those work using the principles of electromagnetism.0630

Let us do some examples.0642

Find the magnetic flux through a circular wire of radius 0.2 m sitting in a 3 T uniform magnetic field if the circle of wire is tipped 20 degrees from the horizontal.0644

We are tipped just a little bit here as we come out of our surface compared to the magnetic field and we have an angle between them of 20 degrees.0655

Our magnetic flux, φB or φM, however you want to write it, is BA times the cosine of the angle between those...0666

...which in this case is going to be (B) times the area -- well we have a radius, so the cross-sectional area will be πr² cos(θ), which implies then that the flux is going to be...0674

...well (B) is 3 T × π and our radius is 0.2 m^2> × cos(20 degrees), so I get a magnetic flux of about 0.354 Wb.0690

Let us take this a little further. Let us find the induced EMF in the same situation.0713

We have the same circular wire of radius 0.2 m in the same 3 T uniform magnetic field.0718

What is the induced EMF in the wire if the hoop is rotated from 20 degrees to 70 degrees in 5 s and what is the direction of the induced EMF?0723

Well let us find its magnitude first.0732

We already determined that the initial magnetic flux was going to be 0.354 Wb in our last problem.0734

The final magnetic flux is going to be Bπr², now cos(70 degrees), which turns out to be about 0.129 Wb.0742

The induced EMF then is going to be minus our change in flux divided by time and the change in anything is the final minus the initial, so that is going to be minus...0758

...we have 0.129 Wb - 0.354 Wb/5 s and this is an average value to give us an average induced EMF of 0.045 volts.0774

If we want to find the direction of that -- well we had more flux and now we have less, so we have decreasing flux.0793

Lenz's Law tells us that we want to oppose that, so the opposing induced current is going to want to put more through there and now by the right-hand rule, I point the thumb of my right hand in the direction of that opposing magnetic flux and I will get an induced current flow in that direction as I visualize that.0801

There is the direction of the induced EMF and its potential is 0.045 volts.0823

Let us look at another change in magnetic field situation.0833

A coil of wire with 50 turns, each with a radius of 2.5 cm is situated perpendicular to a 2 T uniform magnetic field.0837

After half a second, the magnetic field has dissipated completely.0846

Determine the average EMF induced in the wire.0850

Our initial magnetic flux is going to be BA or B × πr², which is 2π × 0.025²...0853

...our radius in meters, or 0.00393 Wb for a single coil.0872

Our final flux is going to be 0 because the magnetic field is dissipated, so our average induced EMF is going to be minus...0879

...well we have to take into account our number of coils (N) times the change in flux divided by our time interval or -50, our change in flux...0889

...which is final minus initial or 0 - 0.00393 is just going to be -0.00393 Wb/0.5 s (time interval) or 3.93 volts.0900

Let us try one more example.0920

Looking at the current induced in a rectangular loop of wire, we have a U-shaped loop of wire, which is connected by a conducting path on rails, which moves upward at a constant 3 m/s.0924

So this piece is moving up at 3 m/s.0935

If the wire is situated perpendicular to a uniform 1/2 T magnetic field, find the current flowing through the resistor.0938

In which direction will the current flow?0946

Well, first off, let us figure out that the induced EMF (e-average) is going to be equal to BLV or that is going to be 0.5 T times our length here (0.5 m) times our velocity (3 m/s)...0949

...so 1/2 × 1/2 × 3 = 0.75 volts.0970

Now if that is situated here and we are trying to find the current flowing this must have some resistance in that loop (R).0975

Well (I) is going to be V/R, where induced voltage is just going to be this 0.75 volts over whatever (R) happens to be for that circuit.0983

In which direction will the current flow?0994

To do that we are going to do Lenz's Law again.0996

As (V) is moving up this way, we are getting more flux down through that area; it is getting bigger for a bigger flux.1000

If we want to oppose that, in that case then that means that our induced current is going to want to create a flux coming back out to oppose that and by the right-hand rule, if I point the thumb of my right hand in that direction of the flux from the induced current...1007

... I find that that must be going counter-clockwise so the direction of the induced current would be in that direction.1023

Hopefully that gets you a good start on electromagnetic induction, Lenz's Law, and how we put all of this together.1034

Thanks so much for your time and I look forward to seeing you soon. Make it a great day everyone!1042