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In other words,
the power should scale like V dot, not like V.
Numerically the charge is the same as you would get for
a capacitor, but the field-line pattern is dramatically different.
Subject to a couple of dirty
shortcuts, I get 2.6e-38 watts average power dissipation. I checked
my work using the Maxima computer-algebra system. The code is at
http://www.av8n.com/physics/bob-mag-damping.max
so you can play with it if you want.
So indeed, the damping is small.
Very very small.