Cecil, quit trying to pedal that bull****. The currents at the two
ends of the coil are NOT the same if they are different phases. It is
the phase difference that lets you establish different standing wave
currents at the two ends, when there's a travelling wave in each
direction. So if the phase is different, then clearly there is net
current going into the coil half the cycle, and net current coming out
of the coil half the cycle.

Go ahead and do it with your travelling wave and phasors. It will work
just as well as instantaneous currents. You will find a net current
into the coil at some phase. Clearly the phasor notation is just a
simplification of instantaneous currents for the case of sinusoidal
excitation, and the answers darned well better be the same, or you
better throw out your phasor notation.

OF COURSE the AVERAGE charge in and out is balanced! If it weren't,
then you have a DC current with nowhere to go. This is a linear system
we're modelling here, with no way to convert a sinewave to DC.

So tell us what net AC current into a component represents, and we'll
just about be there.