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Re: [Phys-L] charge versus gorge

I found it very interesting to watch starting up and shutting down the
water pump in a water circuit, and thinking about charge conservation
and self-capacitance. That really helped me concretize the issues of
how Kirchhoff’s laws “break" and how to repair them during transients.
Shutting down the pump usually gets flow of water in both directions
into the reservoir, as well as visually draining vertical tubes illustrating
excess charge accretions maintaining potential (see url)..

Of course the analogy domain and range are limited in many ways,
but I like to think about rich phenomena and water circuits are easy
to observe. The last of an external magnetic field analog in a water circuit is
particularly disappointing.

I had a student write a project about (more intro steady state)
water circuits for his teaching masters’ project recently that might be of interest.

Dan M


On Feb 25, 2021, at 03:07, John Denker via Phys-l <> wrote:

Consider a non-ideal capacitor, namely two solid hemispheres separated
by a small gap.
-- There will be a /mutual capacitance/ between the two hemispheres.
This is what we focus on in an ideal parallel-plate capacitor.
-- Each hemisphere will also have some self-capacitance. Equivalently
we can call this the capacitance between the hemisphere and "chassis
ground", or between the hemisphere and "infinity". We neglect this
contribution for an ideal capacitor.

Ordinary real-world capacitors have an eeeenormous mutual capacitance,
compared to the self-capacitance of the terminals and the wiring. There
is "some" self-capacitance, but in an ordinary well-engineered circuit
this is usually negligible, especially at not-very-high frequencies.

In particular, Kirchhoff's so-called "laws" *demand* that the only
significant capacitance is the mutual capacitance between the plates
of an identified capacitor. They demand that any charge that flows out
of one component immediately flows into some other component, rather than
hanging around on the wiring. The nodes are assumed to have negligible
self-capacitance. This is usually a pretty good assumption, especially
at not-very-high frequencies. This is a good assumption for the circuits
that get built in the introductory physics course.

An upper-division or graduate-level course in RF engineering
is a horse of a different color.

This is why I distinguish between gorge and charge. Current flowing
*through* an ideal capacitor produces equal-and-opposite charge on the
two plates, so if we speak of the capacitor as a whole (or equivalently
a battery as a whole) it is a misnomer to speak of charging or discharging
it. Really we are gorging and disgorging it.

Now you "could" hook both terminals of a capacitor to a van de Graaf
generator and supply some honest-to-goodness charge to it, some free charge,
some unbalanced charge, but that would be a special case. That would be
a spectacular violation of Kirchhoff's "laws".

This sort of loose charge is way, way down on the list of things to worry
about in the circuits we encounter in the elementary class.

Details here:

At the next level, the mutual capacitance and self-capacitance can be nicely
formalized in terms of the /capacitance matrix/.

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