A conducting circular loop is placed in a uniform magnetic field, `B=0.025T` with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of `1 mms^(-1)`. The induced emf when the radius is `2 cm` is

Options

A. `2 pi mu V`
B. `(pi)/(2) mu V`
C. `pi mu V`
D. `2 mu V`

Answer

C

Explanation

The magnitude of the induced e.m.f., `e = (d phi)/dt)`
Let the flux `phi = B cdot A = B cdot pi r^(2)`
`:. e = (d phi)/(dt) = d/(dt)[B cdot pi r^(2)] = 2 pi B r(dr)/(dt)`
In this case, `B= 25 xx 10^(-3) T, r =2 xx 10^(-2)m`
`(dr)/(dt) = 1 xx 10^(-3) m//s`
`:. e = 2 pi xx 25 xx 10^(-3) xx 2 xx 10^(-2) xx 1 xx 10^(-3)`
`:. e = pi xx 10^(-6) V = pi mu V`.