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. `2pimuV`
B. `pimuV`
C. `(pi)/(2)muV`
D. `2muV`

Answer

B

Explanation

Here,
Magnetic field `B=T`
Radius of the loop, `r=2 cmxx^(7)m`
Constant rate at which radius of the loop shrinks,
`(dr)/(dt)1xx^(-3) m s^(-1)`
Magnetic flux linked with the loop is
`phi=Ba cos theta=B(pir^(2))=Bpi2r(dr)/(dt)`
The magnitude of the induced emf is `|epsi|=(dphi)/(dt)=(d)/(dt)(Bpir^(2))(dr)/(dt)`
`=0.025xxpixx2xx2xx10^(-2)xx1xx10^(-3)`
`pixx10^(-6)V=pimuV`