Question

# A flat coil, C of n turn, area A and resistance R, is placed in a uniform magnetic field of magnitude B. The plane of the coil is initially perpendicular to B. The coil is rotated by an angle θ about a diameter and charge of amount Q flows through it. Choose the correct alternatives.

A
θ=90o,Q=(BAn/R)
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B
θ=180o,Q=(2BAn/R)
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C
θ=180o,Q=0
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D
θ=360o,Q=0
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Solution

## The correct options are B θ=360o,Q=0 C θ=180o,Q=(2BAn/R) D θ=90o,Q=(BAn/R)Current through a coil rotating with angular velocity ω is given by:i=nBAωsinωtRCharge flown on rotating the coil through an angle θ is given by:Q=∫idt=∫iωd(ωt)=∫iωdθQ=−nBAcosθR+nBARFor θ=900, Q=−nBAcos 900R+nBAR=0+nBAR=nBARFor θ=1800, Q=−nBAcos 1800R+nBAR=nBAR+nBAR=2nBARFor θ=3600, Q=−nBAcos 3600R+nBAR=−nBAR+nBAR=0

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