In a region of magnetic induction B=10⁻² tesla, a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm, the amplitude of the alternating current induced in the…

Question

In a region of magnetic induction B=10⁻² tesla, a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm, the amplitude of the alternating current induced in the coil is

Accepted Answer

(3) 6 mA. The peak emf of a coil rotating in a uniform field is ε₀=NBAω, with N=1. A=π r²=π(0.3)²=0.09π m². ω=(200×2π)/(60)=(20π)/3 rad s⁻¹. ε₀=10⁻²×0.09π×(20π)/3=0.06π²×10⁻¹=6π²×10⁻³ V. I₀=(ε₀)/R=(6π²×10⁻³)/(π²)=6×10⁻³ A=6 mA. The resistance was chosen as π² precisely so that it cancels.

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