A rectangular copper coil is placed in a uniform magnetic field of induction 40 mT with its plane perpendicular to the field. The area of the coil is shrinking at a constant rate of `0.5m^(2)s^(-1)`. The emf induced in the coil is

Options

A. 10 mV
B. 20 mV
C. 80 mV
D. 40 mV

Answer

B

Explanation

Given, B = 40 mT = `40xx10^(-3)T`
Rate of shrinking of area = `0.5m^(2)s^(-1)`
`rArr" "(dA)/(dt)=0.5m^(2)s^(-1)`
As, `phi=BA cos theta=BA" "[because cos theta=cos 0^(@)=1]`
On differentiating with w.r.t. to t,
`(dphi)/(dt)=B.(dA)/(dt)=e`
`rArr" "e= "induced emf" = 40xx10^(-3)xx0.5=20xx10^(-3)V`
= 20 mV