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

Options

A. `(B_(0)^(2)pir^(2))/(R )`
B. `(B_(0)pi r^(2))/(R )`
C. `(B_(0)^(2)pi r^(4)R)/(5)`
D. `(B_(0)^(2)pi^(2)r^(4))/(R )`

Answer

D

Explanation

Then induced emf E =`(dphi)/(dt)`
`=(d)/(dt) (B.A) = A (dB)/(dt)`
`= (pir^(2))B_(0) (d)/(dt) (e^(-t)) = -pir^(2) B_(0) e^(-1)`
`implies E_(0)= B_(0) pi r^(2) e^(-)I_(tau=0) = B_(0)pi r^(2)`
`:.` The electrical power developed in the resister just at the instant of closing the key = P
`(E_(0)^(2))/(R ) = (B_(0)^(2)pi^(2) r^(4))/(R ) `