The figure shows a rod of length L = 9.64 cm that is forced to move at constant

Question

The figure shows a rod of length L = 9.64 cm that is forced to move at constant speed v = 4.49 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.305 Ohm; the rest of the loop has negligible resistance. A current i = 86.1 A through the long straight wire at distance a = 12.7 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the emf in volts and (b) current in amperes induced in the loop, (c) 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

part A:

induced emf e = lvB

e = 0.0964 * 4.49 * B

here magnetic field B due to Straight current caryingwire is

B = uoi/2pIR

B = (2 *10^-7 * 86.1)/(0.0127)

B = 1.355 mT

So

emf e = 0.0964 * 4.49 * 1.355 *10^-3

emf e = 0.586 mV

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induced currenrt I -= emf/R

I = 0.586 *10^ -6/(0.305)

I = 1.92 uA

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EEnrgy E = = i^2R

E = 1.92 *10^-6 * 1.92 *10^-6 * 0.305

E = 1.12 *10^-12 J

----------------------------------------------------

Force F = iLB

F = 1.92 *10^-6 * 0.0964* 1.355 *10^-3

F = 2.51 *10^-10 N

--------------------------------------------

Power P = Vi

P = 0.586 *10^-3 * 1.92*10^-6

P = 1.12 *10^-9 Watts

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