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

Explanation

`E=(-d phi)/(dt)= -A(dB)/(dt)` (or) `E= -pi r^(2)(d)/(dt)(e^(-t)) implies E=pi r^(2)e^(-t)`
`P=(E^(2))/(R)=(pi^(2)r^(4)e^(-2t))/(R)` at t= 0, `P=(pi^(2) r^(4))/(R)`