Question

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ___ mV.

• A. 13.2
• B. 8.25
• C. 6.6
• D. 1.32

Hint:

For a given perimeter, the circle has the maximum area. Changing shape to square reduces flux.

Answer 1

The Correct Option is D

Initial Area $A_1 = \pi r^2 = \frac{22}{7} (0.07)^2 = 154 \times 10^{-4}$ m$^2$.
Perimeter $L = 2\pi r = 44$ cm. Square side $a = 11$ cm.
Final Area $A_2 = a^2 = (0.11)^2 = 121 \times 10^{-4}$ m$^2$.
$\Delta \Phi = B(A_2 - A_1) = 0.2 (121 - 154) \times 10^{-4} = -6.6 \times 10^{-4}$ Wb.
EMF magnitude $\epsilon = \frac{|\Delta \Phi|}{\Delta t} = \frac{6.6 \times 10^{-4}}{0.5} = 13.2 \times 10^{-4}$ V.
$\epsilon = 1.32 \times 10^{-3}$ V $= 1.32$ mV.