A conducting circular loop is expanding in a magnetic field of 2T uniformly so that rate of increase of its radius R is 1 cm/s. Find the induced emf in the loop when its radius is 20 cm. The field is perpendicular to the plane of the loop.

Options

A. `0.2pixx10^(-2)` V
B. `0.8pixx10^(-2)` V
C. 2.0 V
D. `0.1pixx10^(-2)` V

Answer

B

Explanation

Suppose R is radius of a coil at time t
`phi=AB=pir^2B`
`therefore epsilon=-(dphi)/(dt)`
`=-d/(dt)[pir^2B]`
`=-piB.(d(r)^2)/(dt)`
`=-2piBr. (dr)/(dt)`
`therefore |epsilon|=2pixx2xx0.2xx0.01`
`=8pixx10^(-3)` V
`therefore |epsilon|=0.8pixx10^(-2)` V