A long solenoid of cross-sectional area A and n turns per unit length carries a current that varies as I = I 0 sin(ωt). A small circular coil of N turns and area a (a << A) is placed coaxially inside the solenoid. The peak EMF induced in the small coil is:

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A long solenoid of cross-sectional area A and n turns per unit length carries a current that varies as I = I<sub>0</sub> sin(ωt). A small circular coil of N turns and area a (a << A) is placed coaxially inside the solenoid. The peak EMF induced in the small coil is:

Answer: μ0nNaI0ω.

A μ0nNAI0ω
B μ0nI0ω/a
C μ0NAI0/n
D μ0nNaI0ω

Correct answer: D. μ0nNaI0ω

Explanation: The field inside the solenoid is B = μ0nI, so flux through the small coil is φ = μ0nI×a×N, and peak EMF = N×μ0n×a×(dI/dt)_max = μ0nNaI0ω.

As a magnet approaches a coil, flux rises steadily and a constant non-zero EMF is induced (Faraday's law). Once the magnet stops moving, flux stays constant and the induced EMF drops to zero - EMF only exists while flux is actively changing.

Concept context

Faraday's and Lenz's laws, motional EMF, self/mutual inductance, eddy currents, and the AC generator - how a changing magnetic flux creates an electric current.

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A long solenoid of cross-sectional area A and n turns per unit length carries a current that varies as I = I<sub>0</sub> sin(ωt). A small circular coil of N turns and area a (a << A) is placed coaxially inside the solenoid. The peak EMF induced in the small coil is:

Concept context

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