00:01
All right, so let's say we have two conducting rails with a metal bar across them like this, and there's a magnetic field pointing into the page everywhere like this, and the bars are connected to a resistor that has a value r, and the bar has a mass m and has a length l.
00:24
So we want to know if the bar moves to the right at a speed v, what is the current in the resistor? so the emf as it moves is going to be b times l times v, and so the current is going to be the emf divided by the resistance, so just b times l times v over r.
00:42
And then for part b, in what direction does the current flow? so the current is going to flow upwards as i've drawn it here, because the flux inside this loop is increasing because the area is increasing, so it's going to want to produce its own field that counteracts this flux.
01:02
And so what's the magnitude of the force on the bar? so the force, as you know, is going to be the current times l times b, so you could write it as b l squared times v over r.
01:15
And then if the bar starts off with an initial speed and left a slide, what is its speed as a function of time? so basically what we'll have is m times v dot is equal to b l squared times.....