Chapter 30, Problem 29 In the figure, a metal rod is forced to move with constan

Question

Chapter 30, Problem 29 In the figure, a metal rod is forced to move with constant velocity along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude B = 0.436 T points out of the page. (a) If the rails are separated by 32.4 cm and the speed of the rod is 63.3 cm/s, what is the magnitude of the emf generated in volts? (b) If the rod has a resistance of 17.3 ? and the rails and connector have negligible resistance, what is the current in amperes in the rod? (c) At what rate is energy being transferred to thermal energy?

Explanation / Answer

The area that is enclosed by the rod and rails

A = (v t) L

We can write the magnetic flux

B = B A cos90°

= Bv t L cos90°

= Bv t L

Now that we know the magnetic flux, we can compute the emf

|| = B L v

= 0.436 * 0.324 * 0.633/s

= 0.089 V

Using this emf, we can find the current and power.

i = /R

=  0.089/17.3

= 5.16 mA

P = 2/R

= 0.000457 W

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