A conducing circular loop is placed in a uniform magnetic field of indution `B` tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate `(dr//dt)`. Then the induced e.m.f. at the instant when the radius is `r` is:

Options

A. `pi r B ((dr)/(dt))`
B. `2 pi r B ((dr)/(dt))`
C. `pi r^(2) ((dr)/(dt))`
D. `((pi r^(2))/(2))^(2) ((dt)/(dt))`

Answer

B

Explanation

Here: `A = pi r^(2)`, and `phi = BA = B pi r^(2)`
As `e = (d phi)/(dt) = (d)/(dt) (B pi r^(2)) = pi B (2 r) (dr)/(dt)`
`= 2 pi r B (dr)/(dt)`