A circular coil of radius 10cm with 100 turns carrying a current of 0.5A lies in a magetic field of 2 T such that the normal drawn to the plane of the coil makes an angles `theta` with the direction of the field. Work done in rotating the coil to change the angle `theta` from `0^(@)` to `180^(@)` is

Options

A. `pi J`
B. `2pi J`
C. `4pi J`
D. `8pi J`

Answer

B

Explanation

Given, radius of coil, `R = 10 xx 10^(-2)m`, number of turns in coil, N = 100 turns, current through coil, I = 0.5 A, magnetic field, B = 2T and change in angle of rotating coil, `theta = 0^(@)` to `180^(@)`.
Work done in turning a loop from angle `theta_(1)` to `theta_(2)`.
`W = MB(cos theta_(1) - cos theta_(2))`
`rArr W = NIAB[cos 0^(@) - cos 180^(@)]`
`rArr W = 100 xx 0.5 xx pi xx 100 xx 10^(-4) xx 2[1-(-1)]`
Hence, `W = 2pi J`
`:.` The correct option is (b).