Question

A conducting circular loop of radius $2.2cm$ is placed in a uniform magnetic field of magnitude $0.04T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2mm/s$. The induced emf in the loop when the radius is $2cm$ is

• A. $4.8\pi \mu V$
• B. $0.8\pi \mu V$
• C. $1.6\pi \mu V$
• D. $3.2\pi \mu V$

Answer 1

The correct option is D $3.2\pi \mu V$

Rate of decrease in the radius of the loop is $2mm/s$
Final radius $=2cm=0.02m$
Initial radius $=2.2cm=0.022m$
$e=-\frac{d\varphi }{dt}=-B\frac{dA}{dt}B=0.04T\frac{dA}{dt}=\frac{d}{dt}\left(\pi r^2\right)=\pi \times 2r\frac{dr}{dt}=\pi \times 2\times 2\times {10}^{-2}\times \left(-2\times {10}^{-3}\right)=-8\pi \times {10}^{-5}\therefore e=-0.04\times \left(-8\pi \times {10}^{-5}\right)V=3.2\pi \times {10}^{-6}V=3.2\pi \mu V$