A square loop of side 'a' lying in a perpendicular magnetic field to its plane is changed to a circle. If change occurs in 't' seconds in magnetic field B tesla, the induced emf is 
 

Given data:

A square loop of side ‘a’ 

Concept used: Induced EMF

Detailed solution:

Area of square loop =Area of circle

$4\mathrm{a}=2\mathrm{\pi r}$

$\mathrm{r}=\frac{2\mathrm{a}}{\mathrm{\pi }}$

From the given data, 

$$\begin{gathered} \mathrm{\Delta }\text{A}={\mathrm{a}}^2-{\mathrm{\pi r}}^2 \\ \mathrm{\Delta }\text{A}={\text{a}}^2-\mathrm{\pi }\left(\frac{4{\text{a}}^2}{{\mathrm{\pi }}^2}\right) \\ \mathrm{\Delta }\text{A}={\text{a}}^2\left(1-\frac{4}{\mathrm{\pi }}\right) \end{gathered}$$

Induced$\mathrm{EMF}=\frac{-\text{d}\mathrm{\varphi }}{\text{dt}}$

$\mathrm{EMF}=\frac{-\text{B}\mathrm{\Delta }\text{A}}{\mathrm{\Delta }\text{t}}$

$\mathrm{EMF}=\frac{-\text{B}\times \left({\text{a}}^2\left(1-\frac{4}{\mathrm{\pi }}\right)\right)}{\text{t}}$

$=\frac{-{\text{Ba}}^2}{\text{t}}\left(1-\frac{4}{\pi }\right)$ $=\frac{{\text{Ba}}^2}{\text{t}}\left(\frac{4}{\pi }-1\right)$