Energy Conversion During LC Oscillations

Whenever energy is supplied to a circuit containing a pure inductor L and a capacitor C (with negligible resistance), that energy oscillates back and forth between the inductor's magnetic field and the capacitor's electric field, generating electrical oscillations of a definite frequency called LC oscillations. Assume the capacitor starts FULLY CHARGED with maximum charge $Q_m$: at this instant the energy stored in the capacitor, $U_E=Q_m^2/2C$, is maximum, while the inductor (carrying no current yet) stores zero energy, $U_B=0$ -- the total energy is entirely ELECTRICAL. The capacitor now begins discharging through the inductor, establishing a growing current i (and hence a growing magnetic energy $U_B=Li^2/2$), while its own remaining charge -- and hence its own stored energy $U_E=q^2/2C$ -- correspondingly falls; at any instant during this transfer, the total energy is shared between $U_E$ and $U_B$. Once the capacitor's charge reaches exactly zero, $U_E=0$, and all the energy has transferred to the inductor's magnetic field, now at its own maximum, $U_B=LI_m^2/2$ (with $I_m$ the peak current) -- the total energy is now entirely MAGNETIC. …