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