For more information, please see full course syllabus of AP Physics 1 & 2

For more information, please see full course syllabus of AP Physics 1 & 2

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## Download Lecture Slides

## Table of Contents

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### Intro to Electromagnetic Induction

- Magnetic flux is the amount of magnetic field passing through a specified area.
- Changing magnetic flux creates an induced potential difference known as the induced EMF.
- Lenz's Law states that the direction of the induced current always opposes the change in magnetic flux.
- Electric generators work by turning a coil of wire in a magnetic field to generate an induced emf.

### Intro to Electromagnetic Induction

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
- Objectives
- Induced EMF
- Charges Flowing Through a Wire Create Magnetic Fields
- Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
- Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
- Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
- Finding the Magnetic Flux
- Calculating Induced EMF
- Induced EMF in a Rectangular Loop of Wire
- Lenz's Law
- Electric Generators and Motors
- Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field
- Generators Use Mechanical Energy to Turn the Coil of Wire
- Electric Motor Operates Using Same Principle
- Example 1: Finding Magnetic Flux
- Example 2: Finding Induced EMF
- Example 3: Changing Magnetic Field
- Example 4: Current Induced in a Rectangular Loop of Wire

- Intro 0:00
- Objectives 0:09
- Induced EMF 0:42
- Charges Flowing Through a Wire Create Magnetic Fields
- Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
- Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
- Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
- Finding the Magnetic Flux 1:36
- Magnetic Field Strength
- Angle Between the Magnetic Field Strength and the Normal to the Area
- Calculating Induced EMF 3:01
- The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux
- 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
- Generators Use Mechanical Energy to Turn the Coil of Wire
- Electric Motor Operates Using Same Principle
- 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

### AP Physics 1 & 2 Exam Online Course

### Transcription: 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 Tm ^{2}.*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 πr ^{2} 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 Bπr ^{2}, 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 × πr ^{2}, which is 2π × 0.025^{2}...*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

1 answer

Last reply by: Professor Dan Fullerton

Thu Apr 14, 2016 11:52 AM

Post by Sarmad Khokhar on April 14, 2016

Why isn't it BAcos(alpha) in 4:25

1 answer

Last reply by: Professor Dan Fullerton

Sun Jun 29, 2014 7:49 AM

Post by Lalit Shorey on June 28, 2014

When you first explained Lenz's law I don't understand the circular direction with the right hand rule. How do you still determine the direction it moves in with the direction of the flux?

1 answer

Last reply by: Hoa Huynh

Wed May 7, 2014 7:09 AM

Post by Hoa Huynh on May 5, 2014

Example 2,we find phi(B) = BA cos (alpha); example 3, when B perpendicular to A, is it not that cos (alpha) = 0? why don't we have cos (alpha) on it? Please, explain me

1 answer

Last reply by: Professor Dan Fullerton

Sun Mar 23, 2014 11:41 AM

Post by Lin Jiang on March 23, 2014

For Example 3ï¼Œ I got 0.393V