Question

A wire in the form of a circular loop of radius $10cm$ lies in a plane normal to a magnetic field of $100T$. If this wire is pulled to take a square shape in the same plane in $0.1s$, find the average induced emf in the loop.

• A. $8.99V$
• B. $4.33V$
• C. $7.77V$
• D. $6.74V$

Answer 1

The correct option is D $6.74V$

$2\pi R=4L$

$\therefore L=\frac{\pi R}{2}=\frac{\left(\pi \right)\left(10\right)}{2}=\left(5\pi \right)cm$

$\Delta S=S_i-S_f={(\pi R}^2)-L^2$

$=\pi {\left(0.1\right)}^2-{\left(5\pi \right)}^2\times {10}^{-4}=0.0067m^2$

$e=\frac{\Delta \varphi }{\Delta t}=B\left(\frac{\Delta S}{\Delta t}\right)=\frac{100\times 0.0067}{0.1}=6.7V$