Question

A conducting circular loop is placed in a uniform magnetic field B = 0.025T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 1 mm s${}^{-1}$. The induced emf in the loop when the radius is 2 cm is:

• A. $2\pi \mu V$
• B. $\pi \mu V$
• C. $\frac{\pi }{2}\mu V$
• D. $3.2\pi \mu V$

Answer 1

The correct option is A $2\pi \mu V$

Given:

$B=0.025$

$\frac{dr}{dt}=1mm/s$

$EMF{e}_{r=2cm}=$

$e=\frac{d\varphi }{dt}=\frac{d}{dt}\left(B\pi r^2\right)$
$=2\pi rB\frac{dr}{dt}$
$=2\times \pi \times 2\times {10}^{-2}\times 2.5\times {10}^{-2}\times 2\times {10}^{-3}$
$=2\pi \times {10}^{-6}\pi V=2\pi \mu V$