Electromagnetic Induction

JEE Main level, single correct, medium

6 of 153

Question 6 of 153

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.

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Answer: (B) 1.32

Circular loop with radius r=0.07r = 0.07 m in magnetic field B=0.2B = 0.2 T.
Initial flux through circular loop: Φ1=B×πr2=0.2×π(0.07)2=0.000980π\Phi_1 = B \times \pi r^2 = 0.2 \times \pi(0.07)^2 = 0.000980\pi Wb
The loop is converted to a square maintaining the same perimeter: C=2πr=0.14πC = 2\pi r = 0.14\pi m
Side of square: a=0.14π4=0.035πa = \frac{0.14\pi}{4} = 0.035\pi m
Final flux through square loop: Φ2=B×a2=0.2×(0.035π)2=0.2×0.001225π2\Phi_2 = B \times a^2 = 0.2 \times (0.035\pi)^2 = 0.2 \times 0.001225\pi^2 Wb
Evaluating: Φ1=0.2×0.0154=0.00308\Phi_1 = 0.2 \times 0.0154 = 0.00308 Wb
Φ2=0.2×0.001225×9.87=0.00242\Phi_2 = 0.2 \times 0.001225 \times 9.87 = 0.00242 Wb
Change in flux: ΔΦ=0.00308−0.00242=0.00066\Delta\Phi = 0.00308 - 0.00242 = 0.00066 Wb
Average EMF: ε=ΔΦΔt=0.000660.5=0.00132\varepsilon = \frac{\Delta\Phi}{\Delta t} = \frac{0.00066}{0.5} = 0.00132 V =1.32= 1.32 mV

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