In the figure a circular loop of radius r and resistance R is shown. A variable magnetic field of induction `B=e^(-t)` exists inside the loop. If the key (K) is closed at t = 0, the electrical power developed in the circuit at that instant is equal to

Options

A. `(pir^(2))/(R)`
B. `(10r^(3))/(R)`
C. `(pi^(2)r^(4))/(R)`
D. `(10r^(4))/(R)`

Answer

D

Explanation

Induced emf,
`e=-A(dB)/(dt)=-pir^(2)(d)/(dt)(e^(-t))=pir^(2)e^(-t)`
or, `e|_(t=0)=pir^(2)`
Hence, the power developed in the circuit at the instant of closing the key,
`P=((e|_(t=0))^(2))/(R)=(pi^(2)r^(4))/(R)~~(10r^(4))/(R)`