Question

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

• 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 $3.2\pi \mu V$

$B=0.04T\frac{dr}{dt}=2\times {10}^{-3}\frac{m}{s}r=2\times {10}^{-2}mϵ=-\frac{d\Phi }{dt}=-B\frac{dA}{dt}=-B\left(\pi \right)\left(2r\right)\frac{dr}{dt}ϵ=-0.04\pi \times 2\times 2\times {10}^{-2}\times 2\times {10}^{-3}=32\pi \times {10}^{-7}=3.2\pi \mu V$