A metal bar is free to slide without friction along a U-shaped wire as shown in

Question

A metal bar is free to slide without friction along a U-shaped wire as shown in the figure. The magnetic induction is 0.5 T uniform over the region and pointing out of the page. The bar is being pushed at a constant speed of 1.5 m/sec and has a resistance of 2 Ohm. You may ignore the resistance of the wire. a. What is the current in the loop? b. In what direction does the current flow? c. What force is needed to push the bar? d. What power is expended in pushing the bar? e. What power is dissipated in the resistance of the bar?

Explanation / Answer

(A) induced emf, e = B L v

e = 0.5 x 0.10 x 1.5 = 0.075 Volt

I = e / R = 0.075 / 2 = 0.0375 A or 37.5 mA

(B) field is point out and flux is increassing with time.

hence induced current will like that field deu to this current will be into the page.

so current will be clockwise.

(C) F = IL x B = (0.0375 x 0.10) x (0.5)

F = 1.875 x 10^-3 N

(D) P = F.v = 1.875x 10^-3 x 1.5 = 2.81 x 10^-3 W

(e) P = e I = 0.075 x 0.0375

P = 2.81 x 10^-3 W

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