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, [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.
Now, you can do that in several ways.
You can have dB dT, changing the magnetic fields.
This is the area A of the loop. You can change the area.
You can have 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 lengths Y and widths
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
periods. 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 of that flat
surface is then the area which is X times A,
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 got the A, the area, I've got 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 surface. 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, periods
of about one second. That means omega,
two pi divided by the periods, is then about six radians per
second. 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.
See, 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
with a 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 access,
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 this. Don't fall into 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 fields
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 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 [inaudible] zero if you have sixty Hertz.
Does it mean that hundred twenty
times per second there is no light from the light bulb?
No, it 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.
I 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 -- [inaudible] so you can't even
here the music, 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, there 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
these magnetic fields. There's a light bulb here,
twenty watts, and this gentleman is go- what
is your name? Student: Naveen.
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.
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! 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,
the 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]
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 going straight up.
Let my DA, it's perpendicular to the surface,
B 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 this 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 put it to the right, because that force is to
the left, so the force of [inaudible] 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 eight oh one.
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 by 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 current 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.
What you see on the left is the reflection, by the way,
against the magnetic poles. 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 near 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 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 along. 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.
Oh, small detail. I forgot to turn the power on.
[inaudible] 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 one- 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 has
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.