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Re: Capacitor problem, another question



Let me just comment that many of the problems being raised go away if
we free ourselves from macroscopic circuit models and go down to the
particle level. Then no matter how you slice it, you have the radiation
and/or collisional losses associated with moving (accelerating) charges.

Things like capacitors, inductances and resistors say more about our
human modes of macroscopic thinking than about the elemental objective
reality under consideration.

Would you characterize Donald's two capacitor problem as being
particularly unsuited to analysis using lumped circuit parameters
like capacitances and (self)inductance? I would say that it is
just the right sort to be treated in that way.

What you say is, of course, true. The fields generated by
individual particles ultimately govern the physics. In circuit
theory we simplify this analysis by observing coherence in the
motions of these charges. They are confined to wires; it is
unimportant that we examine the details of the potential function
at the surfaces of the wires which is responsible for confinement
of the charges, or the surface charge distributions which are
ultimately responsible for the curious electric fields that are
always parallel to the drift motions of those charges. Specifying
the wire is sufficient for the accuracy desired. Similarly we
know that there is inductance associated with every capacitor,
and capacitance with every inductor. When it becomes impossible
to disentangle these parameters (as in the case of a cavity like
a microwave oven) we stop using circuit analysis and go to
numerical solution of Maxwell's electrodynamics; fields displace
the circuit elements formerly used to localize those fields.

In the final analysis it is all particles, of course, but we
should not throw our hands into the air and abandon simpler
models when they suffice to describe reality. In the case of the
two capacitors lumped parameters suffice.

Leigh