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Question

In a very long solenoid of radius R, if the magnetic field changes at the rate of dBdt, the induced emf for the triangular circuit ABC as shown in the figure is (AB=BC)

A
R2(dBdt)
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B
4R2(dBdt)
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C
12R2(dBdt)
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D
2R2(dBdt)
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Solution

The correct option is A R2(dBdt)
Magnitude of flux induced, E=dϕdt
Since flux, ϕ=B.A
dϕdt=d(B.A)dt
Since area remains constant
dϕdt=AdBdt
Area of triangle ABC, A=122R×R=R2
Therefore E=dϕdt=R2dBdt
Hence option A is correct.

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