A long solenoid having `200` turns per centimeter carries a current of `1.5 A`. At the center of the solenoid is placed a coil of `100` turns of cross-sectional area `3.14 xx 10^(-4) m^(2)` having its axis parallel to the field produced by the solenoid. When the direction of current in teh solenoid is reversed within `0.05 s`, the induced emf in the coil is

Options

A. `0.48 V`
B. `0.048 V`
C. `0.0048 V`
D. `48 V`

Answer

B

Explanation

`B = mu_(0)nI = 4pi xx 10^(-7) xx 200 xx 10^(2) xx 1.5 = 3.8 xx 10^(-2) T`
`phi = BA = 3.8 xx 10^(-2) xx 3.14 xx 10^(-4) = 1.2 xx 10^(-5) Wb`
When the current in the solenoid is reversed, the change in magentic flux,
`d phi = 2xx (1.2 xx 10^(-5)) = 2.4 xx 10^(-5) Wb`
`:.` Induced e.m.f., `e = N ((d phi)/(dt))`
`= 100 xx ((2.4 xx 10^(-5))/(0.05)) =0.048 V`