The figure shows a rod of length L = 10.1 cm that Is forced to move at constant

Question

The figure shows a rod of length L = 10.1 cm that Is forced to move at constant speed v = 7.01 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.438 0; the rest of the loop has negligible resistance. A current i = 92.8 A through the long straight wire at distance a = 10.6 mm from the loop sets up a (no uniform) magnet c field throughout loop, find the (a) magnitude of the emf and (b) current induced In the loop, (e) At what rate is thermal energy generated in the rod' (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?

Explanation / Answer

Magnetic field B at a distance r from the long straight wire is given by the formula

B=( o/4) * 2I/r

where I=92.8 Amp r= 10.6 mm=10.6 * 10-3 m

B= (10-7 * 2* 92.8)/(10.6 * 10-3)

B=17.5 * 10-4 T

Part a) Magnitute of emf is given by e= B l v

v=7.01 m/s l=0.101 m

e=17.5 * 10-4 * 0.101 * 7.01

e=12.39 * 10-4 V

Part B) Current I= e/R=0.438 ohms

I=12.39 * 10-4 /0.438

I=28.28 *10-4 Amp

Part C) rate of thermal energy generated= power=I2 R

P=28.28 *10-4 *28.28 *10-4 *0.438

P=3.5029 * 10-6 W

Part D) Force F=BIL

F=17.5 * 10-4 *28.28 * 10-4 * 0.101

F=49.98 * 10-8 N

Part E) rate at which this force does work = P=F*v

P=49.98 * 10-8 * 7.01

P=3.50 * 10-6 W

GOOD LUCK!!!

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