So last lecture was arguably the most important
of all my lectures. We saw how a changing magnetic field
can produce a current, an induced electric field,
an induced EMF. And Faraday expressed that in his famous law,
his famous equation which we see there on the blackboard. You select a closed loop in your circuit. Any loop is OK. You attach an open surface
to that closed loop. Any open surface is OK. And you then get an EMF in the loop and that's the time derivative of the magnetic flux
through that surface. And the minus sign indicates
that the induced current itself produces a magnetic flux
that opposes the flux change and that we refer to as Lenz's Law. Today, I will expand on this a lot further. So let's start with a conducting loop
and a magnetic field. This is a conducting loop. Let the dimensions be y x and let--
I have a uniform magnetic field. Magnetic field B is like so. And I choose as the perpendicular vector
to my surface, this is the surface that I attach
to that closed loop. I choose it pointing up. And so the angle between dA and B,
say theta [inaudible] B is uniform. So the flux, phi B, is defined as the integral
of B dot dA, over this open surface. Flux is a scalar. It's plus or it's minus or it's zero. Flux has no direction. So the flux in this case would be x y,
which is the area of this loop since the magnetic field is uniform. That's a very easy integral
and then I get the magnetic field B and then I get the cosine of the angle. So now according to Faraday,
it is the time derivative of this quantity that determines the EMF. And you can do that in several ways. You can have dB dt, the change
in the magnetic field. This is the area A of the loop. You can change the area. You can have a dA dt. But you can also change theta. You can have a d theta dt. And I will look at those today. This number here, the way I have chosen my dA,
is a positive number. If somehow this number increases
in positive value, the induced current that is going to run
will try to create a magnetic field to oppose the change. So in that case if the flux,
which is now positive, is getting larger positive, then the current
that's going to run will be in this direction. That's Lenz for you. So it creates by itself, this current will
create a magnetic field in this direction. And if the magnetic flux, which is now positive
the way I've defined it, were decreasing, then the current would go the other way around. Last time, I did several demonstration
whereby we changed B. We had dB dt's. And there was one particular
demonstration that blew your mind and that you will tell your grandchildren about
and that you will always remember, I hope. Today, I'm going to change theta
and I'm going to change the area, which will also give me then induced EMF's
and therefore induced currents into a closed conducting loop. So let me make another drawing
of the closed conducting loop. This has length y and width x
and I'm going to rotate this. My idea is you can see this three-dimensionally. I'm going to rotate this about this axis
with angular frequency omega. Omega is two pi divided by the period. The period is the time of one rotation. Normally we choose for that capital T. I don't want to do that today
because T can confuse you with Tesla. And so I'm going to rotate this around
so the angle theta that you have there, theta, then becomes theta zero plus omega T,
going back to eight oh one. And I choose this theta zero such that a T zero,
I choose my theta to be zero, and so I have nothing to do with theta zero. So what now is the magnetic flux? This is my loop. I have to commit myself to a surface. Well, I will just choose this flat surface,
just like I did there. I chose that flat surface. I'm free to choose any surface,
why not taking the flat one. And so the flux through that flat surface
is then the area which is x times y, that's the area of this loop. And then I have the magnetic field. And then I have cosine omega T. Maxwell tells me it's not the flux that matters. It is the change in the flux that matters. OK, so d phi dt. I get the A, the area,
I get the magnetic field. An omega pops out and I get a sign of omega t
and I get a minus sign. Normally I don't care about minus signs, because I'm only interested in the magnitude
of the induced EMF. I always know in which direction
the current will flow, I really do, because I know Lenz's law. So you should never have too many hang-ups
on those minus signs, but since I'm getting a minus sign out
of this now here, it would be a little foolish
not to put a minus here and make this into a plus because that, then,
according to Faraday is immediately the EMF and that EMF is changing with time
because you have this sign omega t in here. And so the current that is going to flow,
the induced current, which will also be time-dependent, is the EMF divided by the resistance in the loop and this is the total resistance
of that entire network. There could be light bulbs in there,
there could be resistances in there. It's the total resistance. And this current, when I rotate this loop,
is going to alternate in a sinusoidal fashion. And we call that alternating current, AC. That's what's coming out of the wall, AC. Suppose this loop was double and what I mean
by double is the following, that it works like this. Follow my picture closely. I will go slowly. It's like this, like this, like this, so back
and I close it here, so it's one closed loop, but I have two windings. I have to attach a surface
to this closed loop. That's mandatory. Farado-- Faraday insists I attach an open surface
to this closed loop. What will it look like? Well, I advise you to take that, dip it in soap
and look at it and what you will see then, because the soap
will attach everywhere to the closed loop, you're going to see one surface. It's not two separate surfaces. You don't have two separate loops. It's one surface but sort of two layers. One is lower and the other one comes on top. And so, the magnetic flux will double now, because you're going to see that this magnetic
field penetrates both this soap film and the one that is below
and so you get twice the EMF and if you have N windings
in one closed loop, capital N, then the EMF that you get would be N times larger
and you can make N one thousand. There's no problem with that. I'm going to do a demonstration for you whereby
I'm going to use the earth's magnetic field-- and a loop that you see here
that has forty-two windings. So my capital N is forty-two. Not just two like here, but forty-two. And it is circular. It has a radius. I think it's about thirty centimeters. Here you have it. It's about thirty centimeters. So the area, pi r squared,
which is my capital A, pi R squared is about
oh point two eight square meters. You may want to check that. I use the Earth's magnetic field,
which is about half a Gauss, so that's about five times ten to the minus five
Tesla, if we work in SI units. And I'm going to rotate it around with a period,
period of about one second. That means omega, two pi divided by the periods,
is then about six radians per second. Two pi, I call that six for now. And so what is the EMF that I'm going to get
when I rotate it once around per second? Well, the EMF will change as a function of time. We're going to get forty-two, that's N. We're going to get A, that is oh point two
eight. We're going to get B, that is five times ten
to the minus five, and then we're going to get omega,
that is six and then we get this sign of six t. You see the equation there. The only difference is we have a capital N
out here because we have N windings
in the closed loop. And this number here in front of the sign six t,
you should check that, is about three and a half millivolts. Three point five times ten to the minus three
times the sign of six t and that now is in volts. So you get an alternating EMF
positive, negative, and the maximum value that you would get
is three and a half millivolts. If I look at the EMF as a function of time,
it would be something like this. And from here to here, would then be one second
if I really rotated around in one second. And so the current, the induced EMF,
according to Ohm's Law, is always the induced current
times the resistance of the whole loop, so the induced current will also have this shape,
of course. And how high that is depends on how large
R is. The EMF is independent of capital R. The EMF follows exclusively from those numbers. It's the current that depends on what
the resistance is. Suppose now I rotate twice as fast. I double omega. Two things are changing now. For one thing, that the full period now goes
from here to here, only in half a second. But there's something else that changes. The EMF now doubles,
because look at my equation. It's hiding behind the blackboard, I think. There is an omega in there. It's linearly proportional to omega,
because it's d phi dt that matters. The omega pops out
and so you now get double the EMF, so the three and a half millivolts maximum
would become seven and so if I try to make a drawing of that
twice as high here, twice as low here, then you would get something like this
and so this omega is now twice this one. You get double the maximum value of the EMF. We're going to show that here. I'm going to improve on my lights. You see there a current meter
which is sign sensitive, can go to the right, can go to the left. And I'm going to rotate this loop. When you rotate a loop in a magnetic field, you can even rotate it in such a way
that you get no EMF. I can show that to you easily. If this is the loop and if somehow
the magnetic field came in like this, if you rotated this loop now around this axis,
there would never be an EMF, because the DA and B would always be
perpendicular to each other, so there's never any flux
going through this system. No flux change. But of course, if you rotate it around this
direction, it would be fine. So think about that. Don't fall in that trap. You can rotate in such a way
that there is no flux change. We don't have that problem at all because
the magnetic field here on earth, in Boston, doesn't come straight from heaven down,
but it comes rather steep, so there's never any problem here. I don't have to worry about that. So here is that loop, forty-two windings. The scale there is in microamperes,
so if you want to you can calculate what the resistance of the loop is when I rotate,
but that's really not my objective. I want you to see that when I rotate it,
that you get an alternating current. Very modest, because I rotate very slowly. Now I rotate faster
and it is proportional to omega and so if I rotate faster you get a much larger
maximum induced current. A larger EMF, a larger current. I don't know how fast I can go. This is about as fast as I can go. Gets almost up to four microamperes maximum, and so we are producing here AC,
alternating current. We have slipping contacts here so that the
system doesn't break and we could put a light bulb here
somewhere in this line and then the light bulb may glow. In the United States, what comes out of the wall
is sixty Hertz. So that means that the current
through a light bulb becomes zero a hundred twenty times
per second. A hundred twenty times per second do you go
through zero, if you have sixty Hertz. Does it mean that hundred twenty times per
second there is no light from the light bulb? No, that doesn't mean that
because filaments get hot and so they still glow
even when the current is zero. But they don't cool that fast. If you take a fluorescent bulb, then indeed,
fluorescent tube goes completely off and on, hundred twenty times per second and therefore
you can use them very nicely as stroboscopes, but of course the frequency is fixed. You can't change the frequency. It's a hundred and twenty Hertz. So now you're getting the idea of
an electric generator, or what we call, if you want to, a dynamo,
which produces AC. You have a turbine and a turbine rotates
conducting loops in magnetic fields and that according to Faraday
will then produce your EMF. And that runs our economy. You have a permanent magnet
and you rotate conducting loops, windings, in that magnetic field. The higher your magnetic field,
the higher the EMF. The faster you rotate,
the higher the EMF. The more windings you have,
the higher the EMF. And the larger the area of your loops,
the higher the EMF. As you can see on the equation
that I keep hiding, but that's where it is. In the United States we have sixty Hertz
as I mentioned and we are committed to a maximum
voltage coming out, that is the maximum value
that you get from your alternating voltage, of hundred and ten times
the square root of two volts, and we call that hundred ten volts. In Europe, we have fifty hertz
and the maximum voltage there in the oscillation is two hundred and twenty
times the square root of two. You can not change omega and go faster
somewhere where you generate this electricity, because that would have major consequences. Number one, the EMF that comes out of
the wall would go up, so you might blow your television,
your circuits. But besides that, you would change also
the frequency of the alternating current and there are many systems that run in such a
way that they're locked into that frequency, for instance, many electric clocks and certainly
record players if you still have one-- are locked into the sixty Hertz
and so if you were to increase omega your record player would go around faster
and your clocks would go faster. A long time ago, when I came over from Europe,
I brought my record player with me. The record player requires two hundred and
twenty volts, so I bought a transformer here to-- that-- the hundred and ten volts at my home
would become two twenty. That was fine. And so the record player was happy. It was running. But it ran twenty percent too fast
because I had overlooked that there are sixty Hertz here
and fifty Hertz in Europe. It was going a little bit too fast and you know what that means
when it goes too fast [speaks in a high tone voice] ...you can't even hear the music [laughter] and that's exactly what happened
with my record player. So if we look at a power station,
as we discussed earlier in this course, and let us suppose to get some--
some numbers, that the maximum EMF
that the power station produces, let's say, is three hundred kilovolts
which it puts on the line. And let's say we have a-- we have loops
that have an area of about one square meter and that they use magnetic fields
which are let's say half a Tesla. It's by no means unreasonable numbers. And if now you want sixty Hertz frequency,
so your frequency f, sixty Hertz, so your omega is about six times higher,
two pi higher. It's about three hundred sixty radians
per second. If now you have about
seventeen hundred windings and you can check that at home,
then you get your three hundred kilovolts. Power is induced EMF times current
and with Ohm's Law you can replace E by IR and so you get I square R. This is joules per second
and so someone has to do work. Someone has to put in the energy,
for which you need perhaps fossil fuel, have to burn oil or coal
to keep the turbines going, or nuclear energy, or waterfalls,
or winds. But something gotta keep those windings going,
to keep our economy going. A typical power station in this country
has about one thousand, produces about one thousand megawatts. It is about one thousand
times a million joules per second. I have here a generator which is run by manpower
and for this I need a strong man. Who wants to volunteer? You look very strong, there. Ah, you don't want to look at me now. Come on. Every morning we talk a little bit,
but now you didn't see me. This is a power generator, magnetic field. You see the magnet here. And there are current loops, windings
and when you crank this you turn those windings
into this magnetic field. There's a light bulb here, twenty watts,
this gentleman is go-- what is your name? [Student] Naveen. [Lewin] Naveen. That's almost my last name. Can you start turning and see whether
you can produce twenty watts? Put your foot on the--
yeah, yeah, keep going. Ah, man, a little better! Keep going,
that's not twenty watts yet! Are you sure you had a good breakfast
this morning? He's producing twenty-- roughly twenty joules
per second now. Will you stop a minute? We have six light bulbs here. Naveen, be my guest. Hundred twenty watts. Man, where is Superman? I see nothing! Hundred-twenty joules per second,
he doesn't even come close! Keep going, man, keep going. You want me to stop the whole [inaudible],
keep going. Forget it! Forget it. You tried and that's all that matters. [laughter] [applause] But you see how difficult it is to produce
hundred twenty joules per second. Now, think about it, when you run your hundred
watt light bulb at home and you do that for ten hours,
that is one kilowatt hour. That costs you only ten cents. Would you run that ten hours for ten cents?
You can't even do it, man! [laughter] I'll show you something. I do a lot of mountaineering and in the mountains
you want a light that always works. When you need it the most, your batteries are flat,
so you always have with you a dynamo. This is my dynamo, hand-powered. You see that? That is Superman for you! This is a hundred-twenty watt light bulb! And I can keep it going all the time. I can do better for you. I have a radio here. And this radio has a little generator. Magnetic field, constant magnets,
permanent magnet and windings which you turn around and when I do that I do work
and I generate an EMF. I charge batteries. And then I can play this radio. [radio voice] ... political campaign ... excellent fundraiser ...
... associated with it beyond that ... [laughter] I don't know about that. And it's designed in such a way that
if you turn just for a minute that you have several hours
that you can play the radio. It's quite amazing. Now, we're going to change the area. So far we've changed theta. Now we're going to change the area. I have again a conducting loop here. But now I have a crossbar here
which I can move. I can move it with a velocity v in this direction,
or I can move it to the left. Let this be l and let the lengths be x. My surface that I'm going to choose,
I always have to commit to an open surface, is a flat surface. And I'll make life very simple for all of us, let's assume that the magnetic field
is going straight up. Let my dA, it's perpendicular to the surface,
be straight up, B and dA are in the same direction now Makes my life simple. And so what is the flux now,
going through my surface? Well, that's the area, which is l x,
times the magnetic field which I will assume is uniform
throughout this surface. So as simple as you can have it. Faraday says, "I don't care
what the magnetic flux is!" "I want to know how that magnetic
flux is changing." All right, OK, Mister Faraday. d phi dt equals l times B times dx dt. But dx dt is my velocity and so I get here
times the speed. dx dt is the velocity. And this now is the magnitude of the EMF. Notice I don't care about minus signs. I just want to know how large the EMF is
in terms of magnitude. I always know the direction,
because I know if I move this to the right that the flux is positive,
the way I have chosen my dA and as I move it to the right
that flux is increasing and so I know that the current
is going to run like this, which then creates a magnetic field
that opposes the change. And if I go in the other direction
with the velocity, then of course the current will reverse. Phi l x B, I can live with that. d phi dt, I can put a B here,
if you like that, to remind you that we're dealing
with magnetic fluxes, l B v. I'm happy. If I look here at this rod, try to make
you see three dimensionally this rod is coming straight out of the blackboard. Then the current is now coming to you. The magnetic field is pointing straight up, and so remember that the Lawrence force
is always in the direction of I cross B, is in this direction. That means the Lawrence force, F L,
which in this case would be the current, times the length of this bar which is
the length of this bar times B. That is the force that I have to apply
if I pull it to the right, because that force is to the left,
so the force of Walter Lewin is the same but in this direction. I have to overcome the force,
the Lawrence force, in this direction. And so it's clear that I have to do work. I have a force in this direction
and I move it in this direction and so I do positive work. What happens with that work, well,
that comes out in the form of heat in the resistance of this conductor. I'm creating an EMF. A current is going to flow and the power
is the EMF times the current, I square R. It comes out in the form of heat. If I change the direction when I push in,
velocity is now in this direction, then clearly the current is going
to change direction. And so when I push in,
the Lawrence force will also flip over and so the force for me will flip over,
so again I have to do positive work. There's no such thing as a free lunch,
no matter what I do. Whether I pull this way or push in,
I always have to do positive work and that work is always converted then to heat,
in the resistance of that loop. So the work that I do, let me express it
in terms of-- of power. The power that I generate is my force,
dot product with my velocity and remember from 801-- the work that I do is force
over a little element dx. But power is work per unit time,
so the dx dt becomes velocity. And my force and my velocity
are always in the same direction when I push there in this direction
and when I pull there in this direction. I always do positive work. And so the power that I generate is my force. That's the magnitude of my force,
which is I l B times the velocity. But that must also be the EMF
times the current and notice now that the EMF therefore,
I goes, is l times B times v. And so now I have shown you that the EMF
is exactly what I er-- found before in terms of magnitude but now
I have not used Faraday's Law. This is purely a derivation based off
the work that I do and the work per unit time. So it's interesting that you can also think
of it that way. Let me check my equations. E I, I R squared, I can live with that. Power, force dotted with the velocity. I l B v, this is the magnitude of the EMF
and that's fine. If I have a conducting disk, solid disk
and I move that, I try to move it through a magnetic field,
north pole, south pole. This is the magnetic field. It's a little weaker here,
little weaker there. I move this in. Then there comes a time
when this disk is here that magnetic field lines
go through this portion. That means the magnetic flux
through this surface is changing. Lenz doesn't like that. Farado-- Faraday doesn't like that. And so what's going to happen, the current
is going to go around now like this. It's not so easy to precisely determine
how that current exactly flows. But this current will be seen
from above clockwise, so that it produces a magnetic field in this direction
to oppose the change in magnetic flux. And we call these currents eddy currents. Eddy currents. The eddy current produces heat in here. The heat is the product in joules per second
of the power E times I. I squared R always comes down to the same,
so this disk will heat up a little bit. The resistance now is the resistance there. And that means that the disk will slow down. At the expense of kinetic energy,
heat is produced and it won't go as fast
through this field than the situation would be
if there were no field. And we call that magnetic breaking. And you can easily convince yourself,
which you should do at home, that if you look at the current right here
coming out of the blackboard and you calculate the Lawrence force
right there, you will see that the Lawrence force
is in this direction. It's pushing it out. It opposes the motion. And I can demonstrate that to you. I have here a pendulum. The pendulum is a conducting copper plate
like so, which I'm going to swing between
magnetic poles which are here. Going to swing it in this direction. In fact, I have two pendulums,
one whereby this is solid copper and I have another one whereby it is slotted,
like teeth. If I'm going to oscillate this one
in a magnetic field, you're going to get current there,
eddy currents, sometimes clockwise,
sometimes counterclockwise depending upon how the magnetic flux
for that surface is changing. Whether it moves into the magnetic field
or whether it moves out of the magnetic field, it will always oppose its motion. And so it will damp, you will see that. And it's at the expense of kinetic energy,
heat will be produced in this copper. If you do it with something like this,
the damping will be substantially less. Not zero, but substantially less
because now if there is an EMF that wants to drive a current, this current
has to go through this opening which is air which has a huge resistance
and remember, power is E times I. And if the-- and it's I square R and if the,
if the current is extremely low because the resistance is so absurdly high
then you don't dissipate much power and so there's not much damping
and I can show that to you. By the way, this damping, this magnetic damping
is used sometimes for scales that you weigh yourself on so that it doesn't
oscillate for too long so it damps very quickly. So you're going to see the oscillations there
and it's going to be a little dark but that's the best way
that I can make you see it. Turn on the power. So you see there, the loop--
I'll give you a little light. And first I will oscillate it without any
magnetic fields. I can power this magnet because it has solenoids. So we'll just oscillate it, no magnetic fields. Give you a feeling how it oscillates. So this gives you an idea of how it oscillates. And now I will turn on the magnetic field,
now. Just likes going into mud. I'll do it again. Oh, hitting the magnetic poles. We don't want that. Now, amazing, isn't it? And it doesn't matter whether it goes in
or whether it goes out. And now I will use the ones with the teeth,
and you will see there is damping, but it's substantially less, so this is without
magnetic fields. And now with, now. You can see there's damping, but it's nowhere
nearly as much as there was on the one that was-- that didn't have teeth. I have here a remarkable example
of how our economy is run. I have there some windings,
not just some. We don't even know how many, thousands,
copper wire going around, going around, going around, going around. It's one wire and then there is a light bulb
in that loop. And here is a magnet. We don't know the strength, but I would say
it's not more than a kilogauss, probably a little less. And when I move this between these poles, magnetic field let's say is going in this direction. I don't know whether it's in this or that. I don't know the color code. But there is a magnetic field
going through here, so there's a change in the magnetic flux
through this surface. Very crazy surface. If there are a thousand wires, this surface
goes a thousand times like this, remember? And then there is going to be an induced EMF
and there's going to be an induced current and this light will glow a little. If I go in very slowly, you just see teeny
weeny little light. If I go very fast, then the magnetic flux
change is high, high EMF, lot of light. So I'll make it dark, darker,
so that you can see that. Oh, we don't want this. In fact, we don't need that display at all. So, if you can see me, I have it now and I'm
going to bring it in the magnetic poles and I go very slowly. I do it now. You see? I pull out, a little bit of light,
I go in, a little bit of light. I'm right in now, holding it steady,
nothing happens. Why? Because there's no flux change. Magnetic field is very strong now
through these loops. Faraday doesn't care about how strong it is. He only cares about the change. I pull it out, a little bit of light. Put it in, a little bit of light. Whether I pull in or whether I pull out
doesn't matter. If I do it very fast, I may be able to generate
so much current that the bulb may even blow. I'll try that, because I know you like
the idea of breaking things. We all do. You're not alone. Let's see whether I managed. Yes, I did. It's broken now. So you got something for your money,
didn't you. That runs our economy. Windings, conducting windings that are being
moved forcefully through magnetic fields. Faraday was once interviewed by reporters
when he came up with this law and they said to him, "So what? So fine, so you
moved a winding through a magnetic field and so you get a little bit of electricity? So what?" And his answer was, some day you will tax it. And he was right. He had vision. The reporters didn't. Part of life. I can show you another striking example of,
um, of magnetic breaking. I have here a magnet which I can also power
with solenoids and I have here two rings. One ring, which is complete in the sense that
it's like so, a conducting ring. I drop it through the magnetic field
and as the flux is changing the eddy current will flow in such a direction
that it will oppose the change and so it could either be in this direction
or in this direction. I don't know. But it will flow to oppose the change. And so as it enters the magnetic field,
when the flux is increasing, it will be damped. When it is in the magnetic field and the flux
is not changing very much anymore there will be no damping, but when it comes
out of the magnetic field the flux is changing again through the surface. It will be damped again and you can see that. And then I will throw through there another
ring which is the same dimension but this ring has an opening here. Air, the resistance is huge. So the current that is going to flow,
this eddy current, is way lower because the resistance is so high
and so there is no power dissipation because I is so low and so there is no heat
produced at the expense of kinetic energy, so there is no damping. There is no force, no strong force,
that opposes it. And I can show you both. And for this I need the DC power on again,
and we're going to project it there on the wall. I have to wait and see that I get my carbon
arc up. There it comes. So we're going to project this slot which
is the opening between the pole shoes on the wall there,
light off, light off, all off. And you see it there. This is that magnet. And here comes the ring. The ring, that is going to be decelerated
heavily when it goes in. Watch it. [ring bounces on the table] Oh, small detail. I forgot to turn the power on. [laughter] Ah, it... there we go. Power goes on now. Actually, you see now, I did that purposely,
you see now how fast it should go if there is no magnetic field
and now there is a magnetic field. Now, did you notice these three phases? You get damping and then when it is right
in the magnetic field, when there is very little flux change,
then it picks up speed again and then it slows down again. Watch it again. Now, the one with the slot. Amazing, huh? Now mo-- once more th--
one without the slot. Magnetic damping. All of that result of eddy currents,
all of that the result of Faraday's law. Heat is produced at the expense
of kinetic energy. So if I summarize, then when we create
an induced EMF and we run a current, we either have to change magnetic fields in time,
or we have to change the area in time, or we have to change the angle theta,
but we must make a change in the magnetic flux through
an open surface. And the energy that is dissipated
must come from somewhere. When you rotate the coils, when you power
your dynamo, you have to do work. When you move the crossbar around,
you have to do work. When you move the coil as I did there,
in-between the magnetic poles to make the light glow,
you have to do work. You always experience a force that is against
the direction of your motion, which is another manifestation of Lenz's Law. And thank goodness it is that way,
because if it were the other way around, our universe could not exist
and I'll give you an example. Suppose we have a growing magnetic field
somewhere. And this growing magnetic field creates an EMF
and suppose that EMF supports the growth. Then the EMF would produce
a stronger magnetic field and that keeps the EMF going
in exactly the same direction and so the B field would become even
stronger and you get a runaway process. Situation would get out of control. It would also be a violation
of the conservation of energy, and thank goodness
physics is the way it is, because if it weren't that way
you and I wouldn't be here. We couldn't even exist. See you Wednesday.
