The magnetic field of a cylindrecal magnet that has a pole `-` face radius `2.8 cm` can be varied sinusoidally between minimum value `16.8 T` and maximum value `17.2 T` at a frequecy of `(60)/(pi) Hz`. Cross section of the magnetic field created by the magnet is shown. At a radial distance of `2 cm` from the axis find the amplitude of the electric field (in `m N//C` ) induced by the magnetic field variation.

Options

A. `140 m N//C`
B. `245 m N//C`
C. `180 m N//C`
D. `240 m N//C`

Answer

D

Explanation

`intE.dl = -A. (dB)/(dt)`
`E(2pi r) = -17 [(d)/(dt){17 + 0.2 sin (omegat + phi)}]`
`:. E = (-r)/(2) (0.2) omega cos (omegat + phi)`
`:.` magnitude of amplitude `= (r )/(2) (0.2) = 240 m N//C`