Question

A conducting circular loop is placed in a uniform magnetic field, B = .025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s1. The induced e.m.f. when the radius is 2 cm, is

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

Answer 1

Answer: (C)

$\pi \mu V$

$\varphi =\left(B\right)\left(\pi r^2\right)$
$\Rightarrow e=\frac{d\varphi }{dt}$
$=\left(B\right)\left(2\pi r\right)\left(\frac{dr}{dt}\right)$

$=\left(0.025\right)\left(2\pi \right)(2\times {10}^{-2})\left({10}^{-3}\right)$
$=\pi \mu V$