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We know a little bit
about magnets now.

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Let's see if we can study it
further and learn a little bit

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about magnetic field and
actually the effects that they

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have on moving charges.

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And that's actually really how
we define magnetic field.

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So first of all, with any field
it's good to have a way

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to visualize it.

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With the electrostatic fields
we drew field lines.

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So let's try to do the same
thing with magnetic fields.

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Let's say this is
my bar magnet.

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This is the north pole and
this is the south pole.

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Now the convention, when we're
drawing magnetic field lines,

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is to always start at the north
pole and go towards the

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south pole.

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And you can almost view it as
the path that a magnetic north

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monopole would take.

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So if it starts here-- if a
magnetic north monopole, even

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though as far as we know they
don't exist in nature,

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although they theoretically
could, but let's just say for

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the sake of argument
that we do have a

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magnetic north monopole.

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If it started out here, it would
want to run away from

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this north pole and would try
to get to the south pole.

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So it would do something,
its path would look

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something like this.

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If it started here, maybe
its path would look

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something like this.

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Or if it started here, maybe
its path would look

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something like this.

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I think you get the point.

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Another way to visualize it is
instead of thinking about a

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magnetic north monopole and the
path it would take, you

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could think of, well, what if
I had a little compass here?

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Let me draw it in a
different color.

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Let's say I put the
compass here.

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That's not where I
want to do it.

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Let's say I do it here.

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The compass pointer will
actually be tangent to the

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field line.

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So the pointer could
look something like

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this at this point.

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It would look something
like this.

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And this would be the north pole
of the pointer and this

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would be the south pole
of the pointer.

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Or you could-- that's how north
and south were defined.

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People had compasses, they said,
oh, this is the north

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seeking pole, and it points
in that direction.

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But it's actually seeking
the south pole

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of the larger magnet.

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And that's where we got into
that big confusing discussion

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of that the magnetic geographic
north pole that

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we're used to is actually the
south pole of the magnet that

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we call Earth.

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And you could view the last
video on Introduction to

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Magnetism to get confused
about that.

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But I think you see
what I'm saying.

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North always seeks south the
same way that positive seeks

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negative, and vice versa.

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And north runs away
from north.

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And really the main conceptual
difference-- although they are

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kind of very different
properties-- although we will

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see later they actually end up
being the same thing, that we

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have something called an
electromagnetic force, once we

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start learning about Maxwell's
equations and

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relativity and all that.

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But we don't have to worry
about that right now.

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But in classical electricity and
magnetism, they're kind of

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a different force.

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And the main difference--
although you know, these field

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lines, you can kind of view
them as being similar-- is

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that magnetic forces always come
in dipoles, soon. while

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you could have electrostatic
forces that are monopoles.

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You could have just a positive
or a negative charge.

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So that's fine, you say,
Sal, that's nice.

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You drew these field lines.

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And you've probably seen it
before if you've ever dropped

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metal filings on top
of a magnet.

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They kind of arrange themselves

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along these field lines.

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But you might say, well,
that's kind of useful.

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But how do we determine the
magnitude of a magnetic field

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at any point?

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And this is where it
gets interesting.

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The magnitude of a magnetic
field is really determined, or

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it's really defined, in terms of
the effect that it has on a

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moving charge.

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So this is interesting.

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I've kind of been telling you
that we have this different

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force called magnetism that
is different than the

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electrostatic force.

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But we're defining magnetism in
terms of the effect that it

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has on a moving charge.

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And that's a bit of a clue.

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And we'll learn later, or
hopefully you'll learn later

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as you advance in physics,
that magnetic force or a

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magnetic field is nothing but an
electrostatic field moving

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at a very high speed.

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At a relativistic speed.

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Or you could almost view it as
they are the same thing, just

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from different frames
of reference.

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I don't want to confuse
you right now.

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But anyway, back to what I'll
call the basic physics.

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So if I had to find a magnetic
field as B-- so B is a vector

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and it's a magnetic field-- we
know that the force on a

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moving charge could be an
electron, a proton, or some

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other type of moving
charged particle.

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And actually, this is the basis
of how they-- you know,

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when you have supercolliders--
how they get the particles to

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go in circles, and how they
studied them by based on how

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they get deflected by
the magnetic field.

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But anyway, the force on a
charge is equal to the

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magnitude of the charge-- of
course, this could be positive

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or negative-- times, and this is
where it gets interesting,

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the velocity of the charge
cross the magnetic field.

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So you take the velocity of the
charge, you could either

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multiply it by the scalar first,
or you could take the

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cross product then multiply
it by the scalar.

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Doesn't matter because
it's just a number,

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this isn't a vector.

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But you essentially take the
cross product of the velocity

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and the magnetic field, multiply
that times the

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charge, and then you get the
force vector on that particle.

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Now there's something that
should immediately-- if you

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hopefully got a little bit of
intuition about what the cross

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product was-- there's something

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interesting going on here.

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The cross product cares about
the vectors that are

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perpendicular to each other.

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So for example, if the
velocity is exactly

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perpendicular to the magnetic
field, then we'll

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actually get a number.

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If they're parallel, then the
magnetic field has no impact

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on the charge.

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That's one interesting thing.

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And then the other interesting
thing is when you take the

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cross product of two vectors,
the result is perpendicular to

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both of these vectors.

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So that's interesting.

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A magnetic field, in order to
have an effect on a charge,

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has to be perpendicular
to its you velocity.

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And then the force on it is
going to be perpendicular to

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both the velocity of the charge
and the magnetic field.

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I know I'm confusing you at
this point, so let's play

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around with it and
do some problems.

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But before that, let's figure
out what the units of the

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magnetic field are.

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So we know that the cross
product is the same thing as--

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so let's say, what's the
magnitude of the force?

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The magnitude of the
force is equal to?

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Well, the magnitude of the
charge-- this is just a scalar

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quantity, so it's still just
the charge-- times the

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magnitude of the velocity times
the magnitude of the

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field times the sine of the
angle between them.

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This is the definition of a
cross product and then we

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could put-- if we wanted the
actual force vector, we can

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just multiply this times the
vector we get using the

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right-hand rule.

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We'll do that in a second.

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Anyway we're just focused
on units.

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Sine of theta has no units so
we can ignore it for this

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discussion.

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We're just trying to figure
out the units of

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the magnetic field.

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So force is newtons-- so we
could say newtons equals--

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charge is coulombs, velocity is
meters per second, and then

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this is times the-- I don't know
what we'll call this--

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the B units.

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We'll call it unit sub B.

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So let's see.

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If we divide both sides by
coulombs and meters per

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second, we get newtons
per coulomb.

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And then if we divide by meters
per second, that's the

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same thing as multiplying
by seconds per meter.

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Equals the magnetic
field units.

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So the magnetic field in SI
terms, is defined as newton

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seconds per coulomb meter.

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And that might seem a little
disjointed, and they've come

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up with a brilliant name.

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And it's named after a deserving
fellow, and that's

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Nikolai Tesla.

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And so the one newton second
per coulomb meter is

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equal to one tesla.

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And I'm actually running out of
time in this video, because

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I want to do a whole
problem here.

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But I just want you to sit and
think about it for a second.

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Even though in life we're used
to dealing with magnets as we

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have these magnets-- and they're
fundamentally maybe

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different than what at least we
imagine electricity to be--

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but the magnitude or actually
the units of magnetism is

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actually defined in terms of the
effect that it would have

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on a moving charge.

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And that's why the unit-- one
tesla, or a tesla-- is defined

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as a newton second
per coulomb.

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So the electrostatic charge
per coulomb meter.

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Well, I'll leave you
now in this video.

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Maybe you can sit
and ponder that.

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But it'll make a little bit
more sense when we do some

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actual problems with
some actual

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numbers in the next video.

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See

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