Figure shows a zero resistance rod sliding to the right on...

Figure shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.450 m. The rails are connected by a 12.5 Ω resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T. The bar moves with v = 5.00 m/s. Find the a.) emf, b) current, c.) electric power, and d.) magnetic force on the bar. Label the direction of the force

Transcript

00:01 There is a metal bar denoted by the poorly drawn scribble with a vector labeled v that is moving along two metal rails.

00:12 And the two metal rails are connected by a 12 .5 oom resistor.

00:17 And throughout this entire system, there is an external b field or magnetic field coming out of the page towards you with a magnitude of 0 .75 tesla.

00:31 The bar is moving to the right with a velocity of 5 meters per second, and the two rails that the bar is moving on is separated by a distance of 0 .45 meters.

00:47 We would first like to find the emf denoted by this fancy e right here, and there is a way to derive the actual equation we are going to get for this, but essentially what you would do there is we know that magnetic flux is equal to magnetic field times area and you would have to think about the area of the rail as it changes.

01:19 What is changing there? that's a problem for you to solve on your own time because essentially what you are going to get is emf is equal to magnetic field times like.

01:34 Length times velocity.

01:38 So we know all these values.

01:41 So we know that emf is equal to 0 .75 teslas, 0 .45 meters, and 5 meters per second.

02:00 So we get that em, that the induced emf in the circuit that we are creating by putting the bar on the rails is roughly 1 .5.

02:10 6 -9 volts.

02:12 Next, we would like to find current.

02:15 And fortunately, this is a tiny bit easier.

02:18 We just use oms law.

02:20 So we use voltage equals current times resistance.

02:24 And we know that this voltage is the same as induced emf in this case.

02:31 So we are going to have induced emf equals current times resistance.

02:36 And we would like current because we have resistance.