A circular loop of radius R is placed in the uniform magnetic field. The value of magnetic field changes is given by equation `B=B_0 e^(-t/tau)` . Where `B_0` and `tau` are constants. The emf induced in the coil is ____

Options

A. `pi^2B_0 e^(-t/tau) xx 10^(-2)` V
B. `(piR^2B_0)/tau e^(-t/tau)`
C. `pi^2B_0 tau e^(-t/tau)`
D. None of these

Answer

B

Explanation

`phi=AB=pir^2B_0 e^(-t/tau)`
`therefore epsilon=-(dphi)/(dt)`
`=-d/(dt)[pir^2B_0 e^(-t/tau)]`
`therefore epsilon=-piR^2B_0 d/(dt)(e^(-t/tau))`
`=-piR^2B_0 (-1/tau.e^(-t/tau))`
`therefore epsilon=(piR^2B_0)/tau e^(-t/tau)`