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. `2pi mu V`
B. `pi mu V`
C. `pi/2 mu V`
D. `2mu V`

Answer

B

Explanation

Here , magnetic field, B = 0.025 T
Radius of the loop , r = 2cm ` = 2 xx 10^(-2) m`
constant rate at which radius of the loop shrinkes,
`(dr)/(dt) = 1 xx 10^(-3) ms^(-1)`
Magnetic flux linked with the loop is
`phi = BA cos theta = B (pir^2) cos 0^@ = B pi r^2`
The magnitude of the induced emf is
`|epsi| = (dphi)/(dt) = (d)/(dt) (B pi r^2) = B pi 2r (dr)/(dt)`
`= 0.025 xx pi xx 2 xx 2 xx 10^(-2) xx 1 xx 10^(-3)`
` = pi xx 10^(-6) V =pi mu V`