Hi. It's Mr. Andersen and this is AP Physics essentials video 32. It is on the magnetic
field of a wire. Scientists for years and years and years knew there was some link between
magnetism and electricity. But they could not find it. There were a lot of clues that
pointed in that direction. If you take two magnets, let them go, North goes to South,
just like positive goes to negative. If you pull them apart there is a force between the
two. And that force gets greater the closer those two magnets get together. It is just
like charges. There is an attraction between the two. And actually Coulombs Law applies
to both magnetic fields and magnetic forces and electric fields. What they also knew is
that magnetic fields are created and can be measured using a compass. So if you took a
bar magnet like this and move a compass around it, you can see that it is lining up with
that magnetic field. And so what they wondered is, maybe if we take a compass and move it
next to a charged object, as we move it around that charged object it is going to point towards
the charged object, but it is simply did not. And so it did not seem like charges were producing
any kind of a magnetic field. And then a brilliant Danish scientist named Hans Christian
\fs30 \'d8rsted \fs28 moved the charge. And so what he has
here is a current. So we have got a current or we know now that it is electrons that are
moving. But the conventional current is going to be in this direction. And so what he found
is that as the current moved through the wire it actually deflected a compass. So that particle,
that charged particle has to be moving. And so we could demo this in a science lab. Imagine
if we have a wire coming out of a table and we just put a bunch of compasses around it.
And so we have the wire coming out of the table. It is coming towards us. And then we
have just lined a bunch of compasses up. But we have not turned on the current. Watch what
happens when we turn on the current in that wire. You can see that we are creating a magnetic
field around the wire and we could measure that and where it is. And so if you have a
wire that is a straight wire, so not a curved wire, and it has a current flowing through
it, then we are going to have a magnetic field that goes around that wire. And we can measure
the magnitude of that magnetic field. And it is really based on two things. The first
one is going to be the amount of charge. And so how much current we have that is moving
through that wire. And there is a direct relationship between the two. The more flow there is, the
more magnitude we are going to have in the magnetic field. And then we have the radius
or the distance from the wire. And so again this wire is in cross-section. And so this
would be the radius or the distance away from that wire. And so there is an inverse relationship
from that. The greater the radius is, the smaller that magnetic field is going to be.
Now how do you figure out which way the magnetic field is going to be? Well the direction is
going to be determined by the right hand rule. And so what you use is your hand again, but
the thumb is going to show where the current is moving. And then the curling of your hands
like this are going to show you where that magnetic field is. And so in this case I know
the magnetic field is going from the left to the right. I can see that on my diagram
right here. And so is the current flowing toward me or away? If I hold my thumb like
this it is coming towards me. So it is coming through the wire at us like that. And so scientists
again figured out that a magnet is going to generate a magnetic field. And so in this
PHET simulation what I am doing is moving the compass around the bar magnet. And you
can see now the south end of the compass is pointed towards the north end of the bar magnet.
But as we move it around to this side, now it is the north end of the compass pointed
at the south end. And so if we look at a simple circuit, so what we have here is a battery
and then a wire that loops back. Watch what happens now when we put a compass and just
kind of move it around this, this is just a simple electromagnet. You can see that it
is not affected by it at all. But once I turn the voltage on then you can see it is really
essentially a magnet. It is a magnetic dipole. And so as we move it around you can see that
compass needle spinning. And so if we turn on the magnetic field you can see where those
field lines are going to be. And I will turn the electrons on as well. You can see it is
being attracted or we are creating a magnetic field. Watch what happens if I turn off that
current. It goes to zero. You can see that there is no magnetic field anymore. If I move
the compass it is not going to respond. Let's move it in the other direction. You can see
now we have those field lines again. What is going to happen if we add more wires? Well,
we are adding more current. And so watch what happens to the electric field. It is getting
greater and greater and greater over time. And so here is that right hand rule. If we
have current moving through a wire, this is conventional current, all you do is just point
your thumb in the direction of where that current is moving. And then as your fingers
curl around it is going to show you where that magnetic field is. And so right here
we have current going up. So I am going to put my thumb up. And so then we have the magnetic
field that is turning around like that. Say the current is going in the other direction,
magnetic field is going to go in the opposite direction. How do we quantify it? Here is
our equation for that magnetic field. It is going to be the magnetic permeability, remember
that is the ability of a material to support a magnetic field. And this is just a free
space. It is going to be one essentially. We then have the current which is going to
be how much electrons or how much conventional current is moving through the wire. Then we
have 2 pi over r. So again, if we increase the radius, we are going to decrease that
magnetic field. If we increase the current, since it is on top of this equation, it is
going to increase the magnetic field. Now you might recognize this on the bottom. What
is 2 pi r? That is going to be the area of a circle. And that is because as we move farther
out from that wire we are going to have a 2 pi r relationship between the amount of
current and then the magnetic field. And so another important thing that you should understand
is if we have multiple wires that are going right next to each other. So let's say we
have a wire and the current is moving from bottom to top. Can you figure out which way
the magnetic fields are going to be? Use your thumb. Point it in the direction of the current
and so you should have your magnetic fields going like that. But let's say we have another
wire right next to it. And it also has current going up. Well what is going on right here
is that we are actually having a magnetic field act on those electrons as they are moving
through this wire. And so we can figure out the direction in which that force is going
to act. And so we are going to use our other right hand rule. Remember that is this right
hand rule, where we point in the direction of the movement of the particle. We then have
our magnetic field represented with our middle finger. And then the force is going to be
your thumb. So it looks like that. So what we have essentially got is the current in
this direction. The magnetic field is going to be in that direction. And so we are going
to get a force, so again I am pointing up like that. I have a magnet field like that.
So the force is actually going to go into the middle of those two wires. And likewise
if we put the other magnetic fields of that wire on, then we are going to get a force
that is pushing towards the middle. So if you have two wires and the current is moving
in the same direction there is going to be a force pulling those wires together. And
so a way to think about that is if the current flows together then the wires go together.
It is going to pull them together. Likewise if we are going in the opposite direction,
if they flow apart then those wires are going to be moving apart, because we are going to
get forces that are moving away from that center. And so did you learn to create a representation
of a magnetic field around a wire or a set of wires? Again, always use your thumb. And
the more current we have the greater that field is and the larger that radius is, the
smaller that magnetic field is going to be. I hope that makes sense.
And I hope that was helpful.