00:01
We're going to be looking at a metal bar moving through a magnetic field pointing into the page.
00:07
And at first, we're not going to have the bar forming part of a circuit, but it's just free to move.
00:14
And we will see that this bar acts like a battery that could drive a circuit, and we will connect it into that circuit.
00:23
But let's say the bar is moving to the right, and there is magnetic field going into the page.
00:29
The equation we want to look at is the magnetic force is charge, velocity, cross, b vector.
00:40
So that metal bar has free charges moving in it.
00:44
And if we use our right -hand rule, which i like to use with my fingers on my right hand, pointing towards the velocity, and letting them curl into the direction of the b, which is into the page, in this situation, then your thumb will wind up pointing in the direction of a plus charge.
01:07
So i get the plus charges getting forced to the upper part of that bar, and likewise the negatives would wind up at the bottom of the bar.
01:18
So there is a charge separation, and that separation stops when the force of the electrical field equates to the magnetic force.
01:34
So there's an electric field that develops between those two separated charges, and that electric force is q times e.
01:46
And that is going to balance the magnetic force, and there will become a static situation.
01:59
Now, because there is an electric field, let's say that the bar has length l.
02:04
Let's just go ahead and call that l, little l.
02:08
We know that there is then going to be a potential difference building up between the ends of the bar.
02:17
Potential difference is electric field time spacing in general.
02:26
Here we're kind of assuming a uniform electric field type situation.
02:32
And so we know what that potential is.
02:36
Let's put in the magnetic portion of that.
02:40
Go back to the magnetic field, since that's what we can measure.
02:45
So if we hook this bar into a circuit, let's just go back, hook it into a resistor.
02:53
That bar will act like a battery.
02:56
So often you'll see books call this e for emf.
03:01
I like to use the term oomph.
03:03
Oops, oomph.
03:05
Let's get that right, not m.
03:09
And so a current will be driven through the circuit.
03:14
And just like any battery, the current will come out of the positive terminal and flow through the resistor, hopefully not a short circuit, and come away, come wrap all the way around into the negative terminal.
03:31
So in order to keep that bar moving, you're going to have to supply the energy or the power the i squared are to keep generating energy.
03:43
So let's see what happens next.
03:46
If you give the bar a shove on the circuit, so we won't go into the details of how it's riding on rails and things like that, conducting rails.
03:58
But let's say you give the bar a shove at t -equal zero, but you don't keep supplying energy.
04:15
What will happen to the bar? so that we are going to need a similar force equation, that the force in a current carrying wire sitting in a magnetic field is i -l -crossed -b, and that's a slightly different situation after the current has been set up...