00:01
Here we'll be reviewing the magnetic force on a current carrying wire and related to some simple mechanics of holding a wire stationary using a magnetic field.
00:14
So it doesn't roll down an incline.
00:17
But magnetic force is given as a cross product between i -l -cross -b.
00:31
So what does i mean? that's just the current.
00:35
L is along the wire, so this is specifically for a long straight wire.
00:45
So the l vector is along the wire with length l, but in the direction of current flow.
00:51
So i and l kind of go together.
00:58
But i, we don't usually like to think of that as a vector.
01:02
And of course, b is the external magnetic field.
01:07
So let's take a look at the wire shown.
01:09
We're looking at it end on, so it extends into the plane of the page.
01:15
And we're looking at the front of it.
01:17
Let's say that the magnetic field is pointing straight up and is uniform, and we'll define a coordinate system with x to the right and y, positive, up.
01:34
We can ask ourselves, what direction must the current flow through the wire in order to lift it? so we are thinking about l cross b.
01:46
So l is in the negative c direction, or l is into the page without the current flowing.
02:00
But let's think through the right -hand rule, and i would take two different scenarios.
02:07
What if the current comes out of the page and b points straight up, which way will the force go? so at that direction, i cross b.
02:25
Whoops, this is b, not force.
02:29
In this case, the force will be to the left.
02:43
And, of course, if the current goes into the page and b points up, the force magnetic will point to the right.
03:03
So which one do you need? well, that depends on what the other forces are.
03:08
So if we draw the forces on this wire, there is the weight mg downwards.
03:19
There's the normal force pointing straight up out of the incline normal to the incline.
03:27
Normal force, we'll call it n.
03:31
And so if we think about equilibrium, which way must the magnetic force point? well, it must point to keep that wire in equilibrium.
03:53
So we're using newton's second law.
03:55
The sum of the forces are equal to zero, is equal to zero.
04:01
Okay, so that tells us that the right picture is to have the current coming out of the page.
04:09
And we'll just go ahead and draw that in.
04:13
But i and b are perpendicular.
04:16
So we can say that the force magnetic is equal.
04:25
To ilb in the minus x direction...