A conducting circular loop is placed in a uniform magnetic field `0.04T` with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at `2mm//sec` . The induced emf in the loop when the radius is `2cm` is

Options

A. `4.8 pi mu V`
B. `0.8 pi mu V`
C. `1.6 pi mu V`
D. `3.2 pi mu V`

Answer

D

Explanation

Induced emf in the loop is given by
`e=-B.(dA)/(dt)` where A is the area of the loop.
`e=-B.(d)/(dt)(pi r^(2))=-B pi 2r (dr)/(dt)`
`r=2cm=2xx10^(-2)m`
`dr=2mm=2xx10^(-3)m`
dt = 1 s
`e=-0.04xx3.14xx2xx2xx10^(-2)xx(2xx10^(-3))/(1)V=3.2pi mu V`