Question

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 a rate of $2mm/s$. Find the induced emf in the loop when the radius of the loop is $2cm$.

• 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 $3.2\pi \mu V$

Given $B=0.04T\frac{dr}{dt}=-2\times {10}^{-3}\frac{m}{s}r=2\times {10}^{-2}m\text{We know that emf induced is rate of change of flux}\text{So}ϵ=-\frac{d\Phi }{dt}=-B\frac{dA}{dt}=-B\left(\pi \right)\left(2r\right)\frac{dr}{dt}ϵ=0.04\pi \times 2\times 2\times {10}^{-2}\times 2\times {10}^{-3}=32\pi \times {10}^{-7}=3.2\pi \mu V$