explain please. Figure shows a rod of length L = 10.0 cm that is forced to move

Question

explain please.

Figure shows a rod of length L = 10.0 cm that is forced to move at constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400 Ohm ; the rest of the loop has negligible resistance. A current i = 100 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current 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

a)

a=10 mm =0.1 cm

Induced emf of the rod

E=(uo*i/2pi)*V*ln(a+L/a)

E=(4pi*10^-7*100/2pi)*5*ln(0.1+10/0.1)

E=4.615*10^-4 V or 461.5 uV

b)

I=E/R =4.615*10^-4/0.4

I=1.1538*10^-3 A or 1.1538 mA

c)

P=I^2*R =(1.1538*10^-3)^2/0.4

P=5.325*10^-6 W or 0.5325 uW

d)

F=P/V =5.325*10^-6/5

F=1.065*10^-7 N

e)

P=5.325*10^-6 W or 0.5325 uW

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