In an oscillating LC circuit, in terms of the charge on the capacitor, we have to find (a) the value of the charge present when the energy in the electric field is one-half that in the magnetic field. (c) We have to find the fraction of a period that must elapse following the time when the capacitor was fully charged for this condition to arise.

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In an oscillating LC circuit variation of charge with time is sinusoidal and can be represented by the function

Energy density in the electric field is

and the energy in the magnetic field is

Let the time be t when the energy in the electric field is one-half that in the magnetic field. We have the condition

This relation will be satisfied when

The charge on the capacitor at this instant will be

Let be the instant when the capacitor was fully charged. At that instant,

Let at ,

The fraction of a period that must elapse following the time when the capacitor was fully charged for this condition to arise will be