In a region of uniform magnetic inductance `B=10^(-2)`tesla. A circular coil of radius `30 cm` and resistance `pi^(2) ohm` is rotated about an axis which is perpendicular to the direction of `B` and which forms a dimater of the coil. If the coil rotates at `200` r.p.m the amplitude of the alternatic current induced in the coil is

Options

A. 200 mA
B. 30 mA
C. `4 pi^(2)mA
D. 6 mA

Answer

D

Explanation

The amplitude of alternating e.m.f. `(E_0) = nAB omega`
`E_(0) = n xx pi r^(2) xx B (2 pi f)`
`:.` Amplitude of AC,
`I_(0) = (E_0)/(R) = (n pi r^(2) xx 2 pi f xx B)/(pi^2) = 2 nr^(2)fB`
`:. I_(0) = 2 xx 1 xx 3/10 xx 3/10 xx 200/60 xx 10^(-2)`
`=6 xx 10^(-3)A = 6 mA`.