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. `(2pirB)/R`
C. `(ralpha)/R`
D. `(pir^(2)alpha)/R`

Answer

D

Explanation

`(dB)/dt=alpha`
`|e|=(dvarphi)/dt=A(dB)/dt=pir^(2)alpha`
`therefore` Current (I) = `e/R=(pir^(2)alpha)/R`.