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Questions  

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B=B0et is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch is equal to

a
B02πr2R
b
B010r3R
c
B02π2r4R5
d
B02π2r4R

detailed solution

Correct option is D

P=e2R;e=−ddt(BA)=AddtBoe−t=ABoe−t⇒P=1RABoe−t2=A2Bo2e−2tRAt the time of starting t = 0 so P=A2Bo2R⇒P=(πr2)2Bo2R=Bo2π2r4R

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