GATE 2015 EE (EE2) – Question 20

Electromagnetic Fields · Biot-Savart law, Ampere law, Curl, Faraday law, Lorentz force · 1 mark · Numerical answer

A circular single turn of radius 1 m rotates at 60 rpm about its diameter along x, as shown. With $\mu_0=4\pi\times10^{-7}$ SI and uniform $\mathbf H=10^7\hat z$ A/m, peak induced voltage in volts is ________.

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Correct answer: 246 to 250

Explanation

Flux-density magnitude is B=μ0H=4π T. The loop area is πr²=π m² and angular speed at 60 rpm is 2π rad/s.

The flux varies sinusoidally as the loop rotates about a diameter, so induced-emf peak is BAω. Therefore Emax=(4π)(π)(2π)=8π³=**248.05 V**, in 246–250 V.

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