Question

The radius of a coil decreases steadily at the rate of ${10}^2$ m/s. A constant and uniform magnetic field of induction ${10}^{3}Wb/m^2$ acts perpendicular to the plane of the coil. The radius of the coil when the induced e.m.f. in the coil is 1 $\mu$ V, is

• A. $\frac{2}{\pi }$ cm
• B. $\frac{3}{\pi }$ cm
• C. $\frac{4}{\pi }$ cm
• D. $\frac{5}{\pi }$ cm

Answer 1

The correct option is D $\frac{5}{\pi }$ cm

$e=\frac{d\varphi }{dt}=\frac{d}{dt}\left(\pi r^{2}B\right)$
$=2\pi rB\frac{dr}{dt}$
$\Rightarrow r=\frac{e}{2\pi rB\frac{dr}{dt}}$
$\Rightarrow r=\frac{{10}^{-6}}{2\pi \times {10}^{-3}\times {10}^{-2}}=\frac{5}{\pi }cm$