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GATE EE 2026 Set 1 — Question 51

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MCQ+2 / -0.67HardFaraday's & Lenz's LawTime-Varying FieldsElectromagnetic Fields

Electromagnetic Fields → Time-Varying Fields → Faraday's & Lenz's Law

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Question

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas a1a_1 and a2a_2 within the loop are subjected to magnetic fields B⃗1=m2sin⁡(ωt)(1x^+0y^+1z^)\vec{B}_1 = \frac{m}{\sqrt{2}} \sin(\omega t) (1 \hat{x} + 0 \hat{y} + 1 \hat{z}), and B⃗2=−n2cos⁡(2ωt+π/4)(0x^+1y^+1z^)\vec{B}_2 = -\frac{n}{\sqrt{2}} \cos(2\omega t + \pi/4) (0 \hat{x} + 1 \hat{y} + 1 \hat{z}), respectively.
A planar loop A in the XY plane containing two sub-regions with areas a1 and a2, with coordinate axes X, Y, Z shown.
What is the expression for the induced rms voltage in loop A?
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