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. `pirB((dr)/(dt))`
B. `2pirB((dr)/(dt))`
C. `pir^(2)B((dr)/(dt))`
D. `pirBr^(2)/(2)((dr)/(dt))`

Answer

B

Explanation

If the radius is `r` at a time `t`, then the instantaneous magnetic flux `f` is given by:
`phi=pir^(2)B`
now, induced `e.m.f.e` is given by
`e=(dphi)/(dt)=-(d)/(dt)(pir^(2)B)=piB(2r(dr)/(dt))=2pirB(2r(dr)/(dt))`
induced e.m.f `2pirBr((dr)/(dt))` numerically`