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