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Question

# A flat circular coil of n turns, area A and resistance R is placed in a uniform magnetic field B. The plane of coil is initially perpendicular to B. When the coil is rotated through an angle of 180o about one of its diameter, a charge Q1 flows through the coil. When the same coil after being brought to its initial position, is rotated through an angle of 360o about the same axis a charge Q2 flows through it. Then Q2/Q1

A
1
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B
2
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C
1/2
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D
0
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Solution

## The correct option is D 0Net charge flowing through the coil is given by Q=ΔϕR where R is the resistanceInitially the plane of ring is perpendicular to B, i.e Area vector →A is parallel to →B where A is the area of the coil.∴ initial flux ϕi=→A.→B=ABCase 1) : Coil is rotated by 180o i.e →A ∥ −→B∴ Final flux ϕf=−AB⟹|Δϕ|=|ϕf−ϕi|=2ABThus Q1=2ABR .............(1)Case 2): Coil is rotated by 360o, i.e →A ∥ →BThus final flux ϕf=AB ∴Δϕ=ϕf−ϕi=0Hence Q2=ΔϕR=0⟹Q2Q1=0

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