Question

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

• A. 27 V
• B. 20 V
• C. 30 V
• D. 22 V

Answer 1

Answer: (A)

If $r$ is radius of circle then side of square = $\frac{2 \pi r}{4} = \frac{\pi r}{2}$
$\therefore $ Change in area = $\pi r^2 - \left( \frac{\pi r}{2} \right)^2 = \frac{\pi (4 - \pi)}{4} r^2$
$\therefore $ E.m.f = $\frac{BA}{t} = \frac{100}{0.1} \times \frac{\pi}{4} (4 - \pi) ( 10 \times 10^{-2} )^2$ = 27V