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Let's say I have a
magnetic field

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popping out of this video.

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So these little brown circles
show us the tips of the

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vectors popping out
of our screen.

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And in that magnetic field I
have this wire, this off-white

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colored wire.

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And sitting on that off-white
colored wire I have a charge

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of charge Q.

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Let me write down
the other stuff.

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So this is the magnetic
field B coming out.

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Let's say I were to take
this whole wire.

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And let's say that the wire
overlaps with the magnetic

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field a distance of L.

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So let's say the magnetic
field stops

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here and stops here.

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And let's say that this distance
right here, that

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distance is L.

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I drew it a little bit weird
but you get the idea.

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From here to here is L.

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I have this charge sitting on
some type of conductor that we

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can consider a wire.

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And the magnetic field is
pushing out of the page.

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So in this current formation,
let's say I don't have any

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voltage across this
wire or anything.

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What's going to happen?

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Well, if I just have a
stationary charge sitting in a

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magnetic field, nothing really
is going to happen, right?

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Because we know that the force
due to a magnetic field is

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equal to the charge times the
cross product of the velocity

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of the charge and the
magnetic field.

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If this wires are stationary and
there's no voltage across

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it, et cetera, et cetera, the
velocity of this charge is

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going to be 0.

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So if the velocity is 0, we know
that the magnitude of a

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cross product is the
same thing as--.

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So Q is, that's just a scalar
quantity-- so that's just Q--

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times the magnitude of the
velocity times the magnitude

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of B times sine theta.

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And in these situations where
anything that's going on in

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this plane is going to
be perpendicular to

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this magnetic field--.

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So the angle between the
magnetic field and any

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velocity-- if there were any
within this plane-- would be

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90 degrees.

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So you wouldn't have to worry
about the sine theta too much.

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But we see if the velocity is
0 or the speed is 0, the

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magnitude of the velocity is 0,
that there's not going to

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be any net force due to the
magnetic field on this charge.

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And nothing interesting's
going to happen.

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But let's do a little
experiment.

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What happens if I were to move
this wire, if I were to shift

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it to the left, with
the velocity V?

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So I take this wire and I shift
it to the left with the

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velocity V.

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All right, so the whole wire
is shifting to the left.

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Well, if the whole wire is
shifting to the left, this

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charge is sitting on that wire,
so that charge is also

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going to move to the left
with the velocity V.

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And now things get
interesting.

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The charge is moving to the left
with the velocity V, so

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now we can apply the
first magnetism

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formula that we learned.

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We could apply this formula.

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So what's going to happen
to this charge?

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Well, the force of the charge
is going to be the charge

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times the magnitude of the
velocity cross the magnetic

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field vector.

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So we know that there's going
to be some net force.

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This is non-zero now.

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And this is non-zero,
we're assuming.

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And we're assuming the
charge is non-zero.

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So what direction is the
force going to be in?

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So let's do our right hand rule
on the cross product.

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V cross B will give
us the direction.

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So point your index finger in
the direction of the velocity.

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I have to look at my own
hand to make sure

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I'm doing it right.

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So you point your index
finger in the

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direction of the velocity.

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Point your middle finger
in the direction of

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the magnetic field.

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The magnetic field is popping
out of the page, so your

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middle finger is actually
going to be

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popping out of the page.

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Your next two fingers
are just going to do

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something like that.

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So you're kind of approximating
like you're

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shooting a gun.

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And then what's your
thumb going to do?

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Your thumb is going to
point straight up.

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This is the palm of--
that's your thumb.

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This could be your nail,
fingernail, fingernail of your

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thumb, fingernail of
your middle finger.

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This is the direction
of the velocity.

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Let me get a suitable color.

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The velocity is that way.

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The magnetic field is popping
out of the page.

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So the force on the particle--
on this charged particle or on

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this charge-- due to the
magnetic field is going to go

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in the direction
of your thumb.

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So the direction of the force
is in this direction.

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So what's going to happen?

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There's going to be a
net force in this

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direction on the charge.

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And the charge is going to
move upwards, right?

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I mean, when you start having
a moving-- you could imagine

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also that you had multiple
charges, right?

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If you had multiple charges
here and you're moving the

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whole wire, all of those
charges are going

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to be moving upwards.

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And what is another way to call
a bunch of moving charges

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along a conductor?

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Well, it's a current, depending
on how much charge

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is moving per second.

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So at least in very qualitative
terms, you see

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that when you move a wire
through a magnetic field or

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when you move a magnetic field
past a wire, right?

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Because they're kind of the same
thing, it's all about the

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relative motion.

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But if you move a wire through
a magnetic field, it is

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actually going to induce
a current in the wire.

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It's going to induce the current
in the wire, and

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actually this is how electric
generators are generated.

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And I'll do a whole series of
videos on how you-- you know,

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if you're using coal or steam or
hydropower, how that turns,

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essentially that turns these
generators around and it

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induces current.

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And that's how we get
electricity from all of these

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various energy sources
that essentially just

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make turbines turn.

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But anyway, let's go back
to what we were doing.

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So let me ask you a question.

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If this particle-- and this
all has a point-- if this

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particle starts at
the beginning.

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Let's say the particle
is right here.

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So it starts right where the
magnetic field starts

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affecting the wire.

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And how much work is going to be
done on the particle by the

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magnetic field?

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Well, what's work?

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Work is equal to force times
distance, where the force has

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to be in the same direction
as the distance, right?

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Force times distance, I
won't mess with the

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vectors right now.

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But they have to be in
the same direction.

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So how much work is going to
be done on this particle?

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So the work is going to be the
net force exerted on the

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particle times the distance.

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Well, this distance
is L, right?

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We say, once a particle gets
here there's no magnetic field

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up here, so the magnetic field
will stop acting on it.

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So the total work done: Work,
which is equal to force times

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distance, is equal to-- so the
net force is this up here.

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Q-- and I'll leave
some space-- V

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cross B times the distance.

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And the distance right here is
just a scalar quantity, so we

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could put it out front, right?

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Q times L times V
cross B, right?

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This is-- Q V cross B is the
force times the distance.

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That's just the work done.

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Now how much work is being
done per charge, right?

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This is how much work is being
done on this charge.

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But let's say there might have
been multiple charges, so we

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just want to know how much
work is done per charge.

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So work per charge.

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We could divide both
sides by charge.

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So work per charge is equal
to this per charge.

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So it is equal to the distance
times the velocity that you're

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pulling the wire to the left
with cross the magnetic field.

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This is where it gets
interesting.

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So what is work per charge?

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The units of work are
energy, right?

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Joules.

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And charge, that's
in coulombs.

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So what are joules
per coulomb?

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This is equal to volts.

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Volts are joules per coulomb.

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So this particle, or these
charges, are going to start

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moving in this direction as if
there is a voltage difference.

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As if there is a potential
difference between this point

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and this point.

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As if this is the positive
voltage terminal and this is

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the minus voltage terminal.

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So there's actually going to be
a voltage-- or a perceived

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voltage-- difference between
this point and this point that

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will start making the
current flow.

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Let's say you didn't even know
that there was a magnetic

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field here.

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You would just see this
current flowing.

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You'd be like, oh well, there
has to be a voltage difference

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there, right?

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But when we're dealing with
this-- because when we talk

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about voltages, that was like
a potential difference.

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That something-- that a particle
or a charge has a

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higher potential energy and
that's why it's moving.

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But it's hard to-- at least for
these purposes-- say, well

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you have a higher potential
energy here.

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It's really being created
by the magnetic field.

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So in this context, people
have said that instead of

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saying that this is creating a
voltage difference between

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this point and this point, if
the magnetic field on the

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moving wire is causing that,
people say that it's creating

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an electromotive force,
or an EMF.

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00:09:06,050 --> 00:09:10,510
But EMF, the units are still
joules per coulomb or volts.

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And it really is-- in every way
when you're analyzing the

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circuits-- still the same
thing as a potential

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00:09:16,240 --> 00:09:18,040
difference or as a voltage
difference.

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00:09:18,040 --> 00:09:20,430
But since it seems a little bit
more proactive, it seems

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like this magnetic field is
actually impacting a force on

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00:09:24,940 --> 00:09:27,030
this wire that is causing
the current to move.

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00:09:27,030 --> 00:09:29,260
We call it EMF.

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00:09:29,260 --> 00:09:34,300
So we could say that the EMF,
the electromotive force-- or

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00:09:34,300 --> 00:09:37,720
the voltage across from here
to here, but they're really

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00:09:37,720 --> 00:09:41,750
the same thing-- is equal to
the distance of the wire

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00:09:41,750 --> 00:09:47,290
that's in the magnetic field
times the velocity-- that

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you're pulling the wire in--
cross the magnetic field.

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So let's say, I don't know,
let's just throw out a bunch

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00:09:54,280 --> 00:09:54,730
of numbers.

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Let's say that the magnetic
field is-- I'll

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make it easy-- 2 teslas.

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My velocity to the left is
3 meters per second.

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00:10:05,340 --> 00:10:08,000
And let's-- just for fun-- let's
give this a little bit

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00:10:08,000 --> 00:10:11,360
of a resistance, just so we
can figure out something.

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So let's say this resistance is,
I don't know, let's say it

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is 6 ohms. There's a 6
ohm resistor here.

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So the resistance of the wire
from here to here is 6 ohms.

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00:10:22,000 --> 00:10:23,970
All wires have some
resistance.

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00:10:23,970 --> 00:10:25,920
So first of all,
what's the EMF?

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00:10:25,920 --> 00:10:27,650
Oh, and let's say that
this total distance

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00:10:27,650 --> 00:10:32,420
right here is 12 meters.

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00:10:32,420 --> 00:10:37,370
So the EMF induced on the-- or
the electromotive force-- put

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00:10:37,370 --> 00:10:40,950
on to the wire by the magnetic
field is going to equal the

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00:10:40,950 --> 00:10:42,980
distance of the wire
in the magnetic

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00:10:42,980 --> 00:10:47,130
field-- 12 meters-- times--.

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00:10:47,130 --> 00:10:48,920
Well, when we're just taking
the cross product, we know

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that the velocity is
perpendicular to

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the magnetic field.

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00:10:53,210 --> 00:10:54,930
So we don't have to worry about
sine theta because theta

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is already 90 degrees.

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00:10:56,240 --> 00:10:57,870
So we just have to worry
about the magnitudes.

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So it's going to be 12 meters
times the velocity, which is 3

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00:11:01,540 --> 00:11:04,660
meters per second, times the
magnetic field, or the

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00:11:04,660 --> 00:11:08,140
magnitude of the magnetic
field, that's 2 teslas.

247
00:11:08,140 --> 00:11:10,390
And so the EMF is 12
times 3 times 2.

248
00:11:10,390 --> 00:11:12,160
12 times 6.

249
00:11:12,160 --> 00:11:14,710
Which is 72.

250
00:11:14,710 --> 00:11:19,770
You could say 72 volts, or
72 joules per coulomb.

251
00:11:19,770 --> 00:11:21,780
And now you have that potential
difference, or that

252
00:11:21,780 --> 00:11:26,640
EMF, across a 6 ohm
resistor, right?

253
00:11:26,640 --> 00:11:29,420
So that, you just go back to
voltage is equal to IR.

254
00:11:29,420 --> 00:11:33,640
Or you could write EMF
is equal to IR.

255
00:11:33,640 --> 00:11:36,300
So EMF divided by resistance.

256
00:11:36,300 --> 00:11:40,440
So if we take this EMF and we
divide it by the resistance--

257
00:11:40,440 --> 00:11:44,430
divided by 6 ohms-- we get
the current, right?

258
00:11:44,430 --> 00:11:48,160
EMF divided by resistance
is equal to current.

259
00:11:48,160 --> 00:11:52,550
So you divide 72 volts or 72
joules per coulomb divided by

260
00:11:52,550 --> 00:11:56,970
6 ohms. And then you get a
current going along this wire

261
00:11:56,970 --> 00:11:59,590
right here, due to the EMF, due
to the magnetic field-- I

262
00:11:59,590 --> 00:12:03,770
know it's very messy at this
point-- of 12 amperes.

263
00:12:03,770 --> 00:12:05,450
Anyway, I'm all out of time.

264
00:12:05,450 --> 00:00:00,000
I'll see you in the
next video.