Question

A conducting circular loop is placed in a uniform magnetic field B$=$ 40 mT with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 2 mms${}^{-1}$, then the induced emf in the loop at an instant when its radius is 1.0 cm is

• A. $0.1\pi \mu V$
• B. $0.2\pi \mu V$
• C. $1.0\pi \mu V$
• D. $1.6\pi \mu V$

Answer 1

Answer: (D)

$1.6\pi \mu V$

$\varphi =B\pi r^2$

emf$=-\frac{d\varphi }{dt}=-2B\pi r\frac{dr}{dt}$

emf at $r=1cm=-2\times 0.04\pi \times 0.01\times 0.002$
$=1.6\pi \mu V$