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Question

There is a uniform magnetic field B in a circular region of radius R as shown in figure, whose magnitude changes at the rate of dB/dt. The emf induced across the ends of a circular concentric conducting arc of radius R1 having angle θ as shown (OAO=θ) is
222626.PNG

A
θ2πR21dBdt
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B
θ2R2dBdt
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C
θ2πR
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D
None of these
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Solution

The correct option is B θ2R2dBdt
Consider the region OAO'
Magnetic Flux
ϕ=B.dA=BA=Bθ2ππR2
ϵ=dϕdt=d(Bθ2ππR2)dt=θR22dBdt
357425_222626_ans.png

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