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Q.

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B = B0e-t is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

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a

B02πr2R

b

B010r3R

c

B02π2r4R5

d

B02π2r4R

answer is D.

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Detailed Solution

P=ε2R;ε=−ddt(BA)=-AddtBoe−t=ABoe−t⇒P=1RABoe−t2=A2Bo2e−2tRAt the time of starting  t=0 so P=A2Bo2R⇒P=πr22Bo2R=Bo2π2r4R
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