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Question:

A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is?

√LC

π/4√LC

π√LC

2π√LC

Solution:

Given Uelectric = Umagnetic
Uelectric = UTotal/2
q2/2C = q02/2(2C)
Thus q = q0/√2
Charge on the capacitor varies sinusoidally.
ω = 1/√LC
q = q0 cosωt (As initial charge is maximum)
cosωt = 1/√2
ωt = π/4
⇒ t = π/4ω = π√LC/4