The conducting rod ab shown in Fig. E29.29 makes contact with metal rails ca and db. The apparat

step 1 Okay, so we're going to chapter 29, problem 29. So in this problem, we have a little bar here. A

The conducting rod ab shown in Fig. E29.29 makes contact...

The conducting rod ab shown in $\textbf{Fig. E29.29}$ makes contact with metal rails ca and $db$. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. (a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s. (b) In what direction does the current flow in the rod? (c) If the resistance of the circuit $abdc$ is 1.50 $\Omega$ (assumed to be constant), find the force (magnitude and direction) required to keep the rod moving to the right with a constant speed of 7.50 m/s. You can ignore friction. (d) Compare the rate at which mechanical work is done by the force ($Fv$) with the rate at which thermal energy is developed in the circuit ($I^2R$).

The conducting rod ab shown in $\textbf{Fig. E29.29}$ makes contact with metal rails ca and $db$. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. (a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s. (b) In what direction does the current flow in the rod? (c) If the resistance of the circuit $abdc$ is 1.50 $\Omega$ (assumed to be constant), find the force (magnitude and direction) required to keep the rod
moving to the right with a constant speed of 7.50 m/s. You can ignore friction. (d) Compare the rate at which mechanical work is done by the force ($Fv$) with the rate at which thermal energy is developed in the circuit ($I^2R$).

Transcript

00:01 Okay, so we're going to chapter 29, problem 29.

00:05 So in this problem, we have a little bar here.

00:13 And this is all in a b field that is pointing into the page.

00:22 And they call this point c, this point d.

00:27 And along this, there is a bar.

00:34 And it is moving along at a velocity v in this direction.

00:42 It also tells us the length here is 50 centimeters and magnitude of b is 0 .8 tesla.

00:59 Okay, so it says part a, find the magnitude of the emf induced in the rod when it is moving towards the right with a speed of 7 .5 meters per second.

01:13 So v equals 7 .5 meters per second.

01:17 So we want to use the equation here we've been using that the emf is the miss.

01:28 And we know that the b field and v are 90 degrees apart, so this is all the equation we need.

01:33 We don't need to use the sign part.

01:37 So we know that this is going to give us 7 .5 meters per second times 0 .8 tesla times 0 .5 meters.

01:49 This is 3 .0 volts.

01:57 So now for part b it says, in what direction does the current flow in the rod? so we know that b is into the page, and as it moves to the right, a gets bigger, right? the area, because this is our loop right here, this is our loop.

02:18 The a is getting bigger, the b is constant.

02:21 So that means our flux b is into the page, and it's increasing.

02:28 So using the lenses law, the induced b must be out of the page.

02:36 Okay, so now using the right -hand rule, does a counterclockwise or clockwise point it out of the page? you'll do that and you'll find it's counterclockwise.

02:49 So that means in the rod, if this is moving counterclockwise, it's moving from b to a...

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