7. An N turn metallic ring of radius a, resistance R, and inductance L is held fixed with its
axis along a spatially uniform magnetic field ~B whose magnitude is given by B0 sin(ωt).
(a) Set up the emf equation for the current i in the ring.
(b) Assuming that in the steady state i oscillates with the same frequency ω as the
magnetic field obtain the expression for i.
(c) Obtain the force per unit length. Further obtain its oscillatory part and the time-
averaged compressional part.
(d) Calculate the time-averaged compressional force per unit length given that B0 = 1
tesla, N = 10, a = 10.0 cm, ω = 1000.0 radians/sec, R = 10 Â, L = 100 mH.
(e) Answer the following two questions without providing rigorous justification:
i. For ω/2π = 60 Hz, the ring emits a humming sound. What is the frequency of
this sound.
ii. A capacitor is included in the circuit. How does this affect the force on the ring?
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