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Current time:0:00Total duration:9:00

- We know a little bit about magnets now. Let's see if we can study it further and learn a little bit
about magnetic field and actually the effects that
they have on moving charges. And that's actually really
how we define magnetic field. So, first of all, with any field, it's good to have a way to visualize it. With the electrostatic
fields we drew field lines, so let's try to do the same
thing with magnetic fields. So let's say this is my bar magnet. This is the north pole. And this is the south pole. Now the convention when we're
drawing magnetic field lines is to always start at the north pole and go towards the south pole. And you can almost do it as the path that a magnetic north monopole would take. So if it starts here, for
a magnetic north monopole even though, as far as we know,
they don't exist in nature although they theoretically could, but let's just say for
the sake of argument that we do have a magnetic north monopole. If it started out here, it would want to run
away from this north pole and it would try to get to the south pole. So it would do something, its path would look something like this. If it started here, maybe its path would look something like this. Or if it started here, maybe its path would look something like this. I think you get the point. Another way to visualize it is, instead of thinking about
a magnetic north monopole and the path that it would take, you could think of, "Well, what if I had a
little compass here." Let's say we draw it in a different color. Let's say I put the compass here, field - oh, and that's not
where I wanted to do it. Let's say I do it here. The compass pointer will actually be tangent to the field line. So the pointer could
look something like this, this point would look something like this. And this would be the
north pole of the pointer, and this would be the
south pole of the pointer. Or you could, you know, that's how north and south were defined. People had compasses, they said, "Oh, this is the north seeking pole, "and it points in that direction." But it's actually seeking the south pole of the larger magnet, and
that's where we got into that big confusing discussion of that the magnetic, geographic
north pole that we're used to is actually the south pole of
the magnet that we call earth. And you could view the last video on introduction to magnetism
to get confused about that. But I think you see what I'm saying. North always seeks south, the same way that positive
seeks negative and vice versa. And north runs away from north. And really the main conceptual difference, although they are kind of
very different properties, although we will see later they actually end up being the same thing, that we have something called
an electromagnetic force, once we start learning
about Maxwell's equations and relativity and all of that. But we don't have to worry
about that right now. But in classical
electricity and magnetism, they're kind of a different force. And the main difference,
although these field lines, you can kind of view
them as being similar, is that magnetic forces
always come in dipoles while you could have electrostatic forces that are monopoles. You could have just a
positive or a negative charge. So that's fine. You say, "South, that's nice." You drew these field lines, and you've probably seen
it before if you've ever dropped metal filings on top of a magnet. They kind of arrange themselves
along these field lines. But you might say, "Well,
that's kind of useful, "but how do we determine the magnitude "of a magnetic field at any point?" And this is where it gets interesting. The magnitude of a magnetic
field is really determined, or it's really defined in terms of the effect that it
has on a moving charge. So this is interesting. I've kind of been telling you that we have this different force called magnetism that is different than
the electrostatic force, but we're defining magnetism
in terms of the effect that it has on a moving charge. And that's a bit of a clue. And we'll learn later, or
hopefully you'll learn later, as you advance in physics,
that magnetic force, or a magnetic field, is nothing
but an electrostatic field moving at a very high speed. At a relativistic speed. Or you could almost view it
as they are the same thing, just from different frames of reference. I don't want to confuse you right now. But anyway, back to what
I'll call the basic physics. So, if I defined a magnetic field as B, so B is a vector, it's a magnetic field. We know that the force on a moving charge could be an electron, a proton, or some other type of
moving charged particle. And actually, this is
the basis of how they, you know, when you have supercolliders, how they get the
particles to go in circles and how they study them by based on how they get deflected
by the magnetic field. But anyway, the force
on a charge is equal to the magnitude of the charge, of course this could be
positive or negative, times, and this is where
it gets interesting, the velocity of the charge cross the magnetic field So you take the velocity of the charge, you could either multiply
it by the scalar first, or you could take the cross product then multiply it by the scalar, doesn't matter because
this is just a number, this isn't a vector. But you essentially take the cross product of the velocity and the magnetic field, multiply that times the charge, and then you get the force
vector on that particle. Now there's something
that should immediately, if you hopefully got a little bit of intuition about what
the cross product was, there's something
interesting going on here. The cross product, it cares about the vectors that are
perpendicular to each other. So, for example, if the velocity
is exactly perpendicular to the magnetic field, then
we'll actually get a number. If they're parallel,
then the magnetic field has no impact on the charge. So that's one kind of interesting thing. And then the other interesting thing is when you take the cross
product of two vectors, the result is perpendicular
to both of these vectors. So that's interesting. A magnetic field, in order to
have an effect on a charge, has to be perpendicular to its velocity. And then the force on it is going to be perpendicular to both the
velocity of the charge and the magnetic field. I know I'm confusing you at this point, so let's play around with
it and do some problems. But before that, let's figure out what the units of the magnetic field are. So we know that the cross
product is the same thing as, so let's say, what's the
magnitude of the force? The magnitude of the force, and I'm going to
arbitrarily change colors, is equal to, well, the magnitude of the charge,
this is just a scalar quantity, so it's still just the charge, times the magnitude of the velocity times the magnitude of the field, times sin of the angle between them. This is the definition of a cross product, and then we could put, if we
wanted the actual force vector, we could just multiply this times the vector we get using
the right hand rule. We'll do that in a second. But anyway, we're just focused on units. Sin of data has no units, so we can ignore it for this discussion. We're just trying to figure out the units of the magnetic field. So force is newtons, so we could say newtons equals charge is coulombs, velocity is meters per second, and then this is times the, I don't know what we'll call this, the B units. We could call 'em units sub B. So let's see. If we divide both sides by
coulombs and meters per second, we get newtons per coulomb, and then if we divide by meters per second that's the same thing as
multiplying by seconds per meter equals the magnetic field units. So the magnetic field, in SI terms, is defined as newton
seconds per coulomb meter. And that might seem a little disjointed, and they've come up with a brilliant name, and it's named after a deserving fellow and that's Nikola Tesla, and so one newton second per coulomb
meter is equal to one tesla. And I'm actually running
out of time in this video, because I want to do a whole problem here, but I just want you to sit and
think about it for a second. Even though in life, we're used
to dealing with magnets as, you know, we have these magnets and they're fundamentally maybe different than what, at least, we
imagine electricity to be, but the magnitude of, or
actually the units of magnetism, is actually defined in terms of the effect that it would have on a moving charge. And that's why the unit
one tesla, or a tesla, is defined as a newton second per coulomb, so the electrostatic
charge, per coulomb meter. Well I'll leave you now in this video. Maybe you can sit and ponder that. But it'll make a little bit more sense when we do some actual problems
with some actual numbers in the next video. See you soon.