Question

A square loop of side $22\text{cm}$ is changed to a circle in time $0.4\text{sec}$ with its plane normal to a magnetic field $0.2\text{T}$. The emf induced is _______$\text{mV}$ ( Only magnitude)

• A. 6.6
• B. 6.60

Answer 1

Answer: (A), (B)

$l=22\text{cm};A_1=l^2=(22\times {10}^{-2}{)}^2{\text{m}}^2$

$A_1=484\times {10}^{-4}{\text{m}}^2$

For a square. $2\pi r=4l$

$\Rightarrow 2\times \frac{22}{7}\times r=4\times 22$

$\Rightarrow r=14\text{cm}$

Area of the circle $A_2=\pi r^2=\frac{22}{7}\times 14\times 14\times {10}^{-4}$

$\Rightarrow A_2=616\times {10}^{-4}{\text{m}}^2$

The induced emf , $e=-\frac{B(A_2-A_1)}{t}=-0.2\left[\frac{616-484}{0.4}\right]\times {10}^{-4}$

$\therefore |e|=+0.2\left[\frac{132}{0.4}\right]\times {10}^{-4}$

$=6.6\times {10}^{-3}\text{V}$

$=6.6\text{mV}$