A 0650 m long metal bar is pulled to the right at a steady...

A 0.650-m-long metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform, 0.750 T magnetic field. The bar rides on parallel metal rails connected through a 25.0-$\Omega$ resistor ($\textbf{Fig. E29.30}$), so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. (a) Calculate the magnitude of the emf induced in the circuit. (b) Find the direction of the current induced in the circuit by using (i) the magnetic force on the charges in the moving bar; (ii) Faraday's law; (iii) Lenz's law. (c) Calculate the current through the resistor.

Transcript

00:01 Here's an example of emotional emf, which usually leads to faraday's law.

00:07 But we can start off with the magnetic force on a moving charge is equal to qb cross b.

00:21 And we can think about what that rod.

00:24 So there's a conducting rod in blue that's being dragged across some metal rails that make complete circuit.

00:33 There is a uniform magnetic field that is shown with the blue crosses into the page.

00:40 And before we get to faraday's law, we can think about what that magnetic force will do to the free charges inside of the moving rod.

00:52 So what will happen is you can use your right -hand rule.

00:56 I like to think about v as the fingers on my right hand.

01:01 And then i have to think about v as the fingers on my right hand.

01:02 To orient them in order to get them to curl into the magnetic field.

01:11 And in order to do that, what i have to do is reorient my hand, let my fingers curl into the page.

01:25 And what that tells me is that the positive charges, if that rod were not connected, the positive charges would flow to the top of the rod.

01:35 Now they are connected, which means that the current will continue to flow up in the rod, connect to the rails, and go all the way around in a counterclockwise direction.

01:55 Let's see if we can figure that out from faraday's law.

01:59 Faraday's law basically gives us a voltage or emf that's induced, and it is negative n, the 9 .0 .0 .5 .5.

02:13 Number of loops times the change in magnetic flux with time.

02:21 N is one.

02:22 There's just one loop.

02:24 And magnetic flux in this case is the magnetic field times the change in the area with respect to time.

02:36 And that area is changing because the rod is moving.

02:43 And so the area is changing by basically the side, what to call that, big l.

02:53 The big l is not changing, but the x is changing, the x coordinate of the rod.

03:00 And that is the velocity.

03:05 And if i think about this, what it says is that the induced emf is going to run in a direction that will be opposite the velocity in the rod.

03:16 That is, if there is a current flowing in that rod, it must create a force on the rod that is pulling it backwards.

03:36 Okay, so the rod is trying to move to the right, and there is a drag force that is going to pull backwards.

03:46 And in order to show that that works, you can use the right -hand rule...

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