CUET and UG exam CUET UG 2025 Mock Test Series Physics Electromagnetic Induction and Inductance Faraday’s Law of Induction
A long solenoid with radius a is driven by an alternating current, generating a sinusoidal magnetic field inside the solenoid, given by\( B(t) = B_0 \cos(\omega t) \hat{z} \) . A circular loop of wire, with radius a/2 and resistance R , is placed inside the solenoid and coaxial with it. What is the induced current in the loop as a function of time?
1
\(I(t) = \frac{\pi a^2 B_0 \omega}{2R} \cos(\omega t).\)
2
\(I(t) = \frac{\pi a^2 B_0 \omega}{2R} \sin(\omega t).\)
3
\(I(t) = \frac{\pi a^2 B_0 \omega}{4R} \cos(\omega t).\)
4
\(I(t) = \frac{\pi a^2 B_0 \omega}{4R} \sin(\omega t).\)