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- [Voiceover] I have an
interesting set up over here.

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I have a magnetic field that is constant,

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and it's going straight out
of the surface of this loop.

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The magnitude of the magnetic field

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at any point of the
surface is going to be 'B'.

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What's interesting here
is this loop that we have,

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This right part of the loop is movable.

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You can imagine it's a cylinder

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that can roll to the right,

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and the magnitude of it's velocity,

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we're going to say is lowercase 'v'.

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And this cylinder, lets
say it has length 'L'

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Given that, you can see that we're going

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to have a change in magnetic flux.

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Why are we gonna have a
change in magnetic flux,

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or a change in magnetic
flux through the surface?

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Well if this thing is moving to the right,

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when it's speed is 'v'

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it can be any units, meters per second,

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or whatever it is.

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Even though the magnetic field itself is

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constant, you're actually
going to be changing the area,

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the area that is, I guess
you could, contained by

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this loop, and so that is going to

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give us a change in flux

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And if you have a change in flux that is

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going to induce an electromotive force,

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or it's going to induce
a voltage in this loop

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which will cause a current to flow.

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Let's think about what
that electromotive force

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that's going to be induced is going to be.

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I'm just gonna rewrite
Faraday's law right over here.

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Faradays law: negative 'N' times

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our change in flux, and we're talking

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about our change in flux over change in,

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let me write that a little bit neater,

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our change in flux over change in time.

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The 'N' is the number of
loops we're talking about.

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So in this case, 'N'
is just going to be one

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and the negative, I've already complained

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a little bit about in previous videos.

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This is really just reminding us

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the math, when you're not using
proper vector mathematics,

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this just reminds us that this 'Emf'

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is going to cause a current
to go through this loop,

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and the magnetic field that is

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induced by that current will
go against the direction

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of our change in flux. That's
just something to remind us.

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What we really care about is

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our change in flux over change in time.

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What is that going to be?

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Let me just write it here,

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our change in flux over change in time.

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Our change in flux in this case

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is going to be our change in

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our, the magnitude of our magnetic field

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that is going perpendicular to the surface

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times the area of our surface

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over our change in time.

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What is this going to be equal to?

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'B' is constant, it's not going to change

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over the time that we care about.

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So the change in 'B' times 'A'

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is really going to be 'B'
times our change in area.

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'B' times our change in area
over how much time goes by.

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So what is our change in area going to be?

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Let's say we let delta 't' ,
let's say delta 't' happens,

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what is going to be our change in area?

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Let's let delta 't' go on.

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If delta 't' goes on, this cylinder,

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or if we wait for 't' units of time,

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or if 't' units of time go by,

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let me do this in another color,

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I'm gonna use this color right over here.

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How far will we go after delta 't'?

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We know the magnitude of our velocity

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if you multiply the
magnitude of your velocity

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times your change in time,

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that will give you your distance.

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Your change in area is going to be

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the amount of distance it's travelled

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times the length of the
rod, which is just that.

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Our change in area, which is
that area right over there,

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our change in area over that time

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is going to be the distance this rod goes.

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Notice this rod is going in a direction

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that is perpendicular to the
direction of the magnetic field

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that's an important thing to realize.

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We have our change in area is going to be

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this dimension which is
how far the rod travels

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times the length of the rod,
that's how much area we gain,

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that's how much our area increases,

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times the length of the rod,
that's our change in area.

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We can substitute that back over here.

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This is going to be equal to,

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we got our 'B', we have
our change in time,

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and our change in area we
just said is going to be,

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Let me just write it this way,

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I could write is as the length of our rod

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times the magnitude of
our velocity, or our speed

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times our change in time.

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Well, change in time
divided by change in time,

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those cancel out. Our change
in flux over that time

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or our average rate of change in flux

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we see simplifies to the length of our rod

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times the magnitude of our velocity,

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or our speed, times the
magnitude of the magnetic field

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that is going perpendicular
to the surface.

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This is something that
you will see many times

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in your physics class,
this whole notion of

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if your rod going in a
perpendicular direction

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to a magnetic field, it induces

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an electromotive force of 'LvB'

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This is where it's coming from,

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it's coming directly from Faraday's law.

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You can say, okay, if that's happening,

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what direction is the current
going to actually flow in?

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If the magnetic field isn't changing,

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but since the area is increasing,

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the flux is increasing
in the upward direction.

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You can say the flux is
increasing in that direction.

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The current that gets induced,

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and the magnitude of the
current is going to be,

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based on how much resistance we have,

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but the current is going
to induce a magnetic field

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that goes against our change in flux.

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Let's see, if the current went
that way, what will happen?

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I'm going to take my right hand out,

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put my thumb in that direction,

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and if I were to loop my fingers around,

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this would, if we went that
way, this would describe,

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this would induce a magnetic field

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that goes like this.

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That actually would enhance

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the flux going through
the, or change in flux,

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going the same direction
of the change in flux,

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We've already talked about this,

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would violate the law of
conservation of energy.

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The current's gonna go
in the other direction.

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It's gonna go, in this case
is going to go clockwise,

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because the current is going
to induce a magnetic field.

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Once again, I could
take my right hand out,

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and try to draw my right hand,

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and we can see now, the direction

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my fingers go in are that way.

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Notice we're looking at
the inside of the surface,

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the surface area was increasing the flux

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in the upward direction, getting more

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of the magnetic field
in the upward direction,

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being contained in the area.

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The magnetic field induced by
the current that is induced,

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or that current that's being caused

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by the electromotive
force and the magnitude of

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the force is going to be
dependent on our resistance,

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that's going to go in the other direction,

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it's going to go down that way.

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Or it's going to induce a magnetic field

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that is gonna go downwards.

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So the current needs
to be going clockwise.