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.
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 view it as the path that a magnetic north
monopole would take.
So if it starts here-- if 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 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 it would take, you
could think of, well, what if I had a little compass here?
Let me draw it in a different color.
Let's say I put the compass here.
That's not where I want 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 at this point.
It 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-- 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 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 you know, these field
lines, you can kind of view them as being similar-- is
that magnetic forces always come in dipoles, soon. 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, Sal, 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 had to find a magnetic field as B-- so B is a vector
and 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 studied 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 it's 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 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.
That's one 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 you 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 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 the sine 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 can
just multiply this times the vector we get using the
right-hand rule.
We'll do that in a second.
Anyway we're just focused on units.
Sine of theta 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'll call it unit 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
Nikolai Tesla.
And so the 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 we
have these magnets-- and they're fundamentally maybe
different than what at least we imagine electricity to be--
but the magnitude 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