A conducting circular loop is placed in a uniform magnetic field `0.04T` with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at `2mm//sec` . The induced emf in the loop when the radius is `2cm` is

Options

A. `3.2pimuV`
B. `4.8pimuV`
C. `0.8pimuV`
D. `1.6pimuV`

Answer

A

Explanation

According to Faraday's second law of electromagnetic induction, the induced emf is given by the rate of change of magnetic flux linked with the circuit.
Here, `B=0.04T` and `(-dr)/(dt)=2ms^(-1)`
induced emf, `e-(dphi)/(dt)=(-BdA)/(dt)=-B(d(pir^(2)))/(dt)`
`=-Bpi2r(dr)/(dt)`
now,`r=2 cm`
`e=-0.04xxpixx2xx2xx10^(-2)xx2xx10^(-3)`
`=3.2pimuV`