GATE 2016 EE (EE2) – Question 65

Electromagnetic Fields · Biot-Savart law, Ampere law, Curl, Faraday law, Lorentz force · 2 marks · Numerical answer

A 1 m conductor rotates about the z axis, parallel to it and 1 m away, in a radially outward 1 T magnetic field as shown. Find rpm needed to induce 1 V along the conductor.

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Correct answer: 9.4 to 9.7

Explanation

Tangential speed at radius r is v=ωr. Its cross product with the radial magnetic field is directed along the axial conductor, with magnitude vB.

The motional emf is e=Blv=B l r ω. With B=l=r=1 and e=1 V, ω=1 rad/s.

Convert to rpm: n=ω60/(2π)=**9.54930 rpm**, within 9.4–9.7.

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