Question

A square loop of side $22\text{cm}$ is changed into a circle in $0.4\text{sec}$, inside a uniform magnetic field of $0.2\text{T}$. The emf induced is,

• A. $6.6\text{mV}$
• B. $3.3\text{mV}$
• C. $1\text{mV}$
• D. $13.2\text{mV}$

Answer 1

The correct option is A $6.6\text{mV}$

Given:

Side of square $a=22\text{cm}$

$\Delta t=0.4\text{Sec}$

$B=0.2\text{T}$

Let the radius of the circular loop be $r$.


Here, the perimeter of the square loop will be equal to the circumference of the circular loop, as the same length of wire is used.

$\Rightarrow 4a=2\pi r$

$\therefore r=\frac{2a}{\pi }=2\times \frac{22}{\pi }=14\text{cm}$

Now, the induced emf is given by,

$E=\left|\frac{\Delta \varphi }{\Delta t}\right|=B\left|\frac{\Delta A}{\Delta t}\right|$

$E=B\left|\frac{\text{Area of square - Area of circle}}{\Delta t}\right|$

$e=0.2\left[\frac{484-\pi \times {14}^2}{0.4}\right]\times {10}^{-4}=6.6\text{mV}$

Hence, option ($A$) is the correct answer.