A long solenoid of radous `R` has `n` turns of wire per unit length and carries a time-varying current that varies sinusiodally as `I = I_(max) cos omegat`, where `I_(max)` is the maximum current and `omega` I the angular frequancy of the alternating current source (shows in Fig.)

The magnitude of the induced electric field inside tha solenoid, a distance `r lt R` from its long central axis is

Options

A. `(3 mu_(0)nI_(max)omega)/(2) r sin omega t`
B. `(mu_(0)nI_(max)omega)/(2) r cos omega t`
C. `mu_(0)nI_(max)omega r sin omega t`
D. `(mu_(0)nI_(max)omega)/(2) r sin omega t`

Answer

D

Explanation

`E = (r )/(2) (dB)/(dt) = (r )/(2) mu_(0)n (dI)/(dt) rArr E = - (mu_(0)nr)/(2) I_(max) omega sin omega t`