Cecil wrote, among other things,
"One amp of forward current is flowing into the coil and one
amp of forward current is flowing out of the coil. Charge is
balanced."

Absolutely NOT! You said the phase difference between the two ends is
45 degrees. Therefore, charge "input" and "output" is balanced ONLY
twice during a cycle, when the instantaneous currents are the same. No
phase need apply he we're talking INSTANTANEOUS currents. The rest
of the time, there's net charge accumulating inside the coil half the
time, and net charge coming out the other half the time. GOT IT yet???
You do NOT need phasor math to do this!

WHAT does that charge represent, Cecil? C'mon, you can say it...

Cheers,
Tom
(Sorry, no prizes. They've already been awarded to John.)