First slide
Magnetic flux and induced emf
Question

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

Moderate
Solution

P=e2R;e=ddt(BA)=AddtBoet=ABoetP=1RABoet2=A2Bo2e2tR

At the time of starting t = 0 so P=A2Bo2R

P=(πr2)2Bo2R=Bo2π2r4R

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