A unifrom magnetic field B points vertically up and is slowly changed in magnitude, but not in direction. the rate of change of the magnetic field is `alpha` .A conducting ring of radius r and resistance R is held perpendicular to the megnetic field, and is totally inside it. The induced current in the ring is

Options

A. zero
B. `(2pieB)/(R)`
C. `(ralpha)/(R)`
D. `(pir^(2)alpha)/(R)`

Answer

D

Explanation

The magnitude of the induced emf in the ring is
`|epsi|=(dphi)/(dt)=(d)/(dt)(BA)=A(dB)/(dt)=pir^(2)alpha`
The induced current in the ring. `I=(|epsi|)/(R)=(pir^(2)alpha)/(R)`