Question

A conducting circular loop is placed in a uniform magnetic field $B=40\text{mT}$ with its plane perpendicular to the field, if the radius of the loop starts shrinking at a constant rate of $2\text{mm/s}$, then the induced emf in the loop at an instant when its radius is $1.0\text{cm}$ is

• A. $0.8\pi \mu \text{V}$
• B. $0.2\pi \mu \text{V}$
• C. $1.6\pi \mu \text{V}$
• D. $0.4\pi \mu \text{V}$

Answer 1

The correct option is C $1.6\pi \mu \text{V}$

Area of circular coil, $A=\pi R^2$

Magnetic flux, $\varphi =BA$

We know that,

${\epsilon }_{ind}=\left|\frac{-d\varphi }{dt}\right|$

$=\frac{d}{dt}\left(B\pi R^2\right)=2B\pi R\frac{dR}{dt}$

$=2\times 40\times {10}^{-3}\times \pi \times {10}^{-2}\times 2\times {10}^{-3}$

$=160\pi \times {10}^{-8}$

$\Rightarrow {\epsilon }_{ind}=1.6\pi \times {10}^{-6}\text{V}=1.6\pi \mu \text{V}$

Hence, option $\left(C\right)$ is correct.