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# Re: [Phys-L] The status of Kirchhoff''s laws

• From: John Denker <jsd@av8n.com>
• Date: Sun, 03 Mar 2013 21:23:28 -0700

On 03/02/2013 08:25 PM, Bruce Sherwood wrote:
An
underappreciated aspect of capacitors in circuits is the role of the fringe
field.

Indeed, the fringe field is important and often under-appreciated.

[lots of good stuff snipped]

Now for the punch line. Suppose in a circuit that more conventional current
is flowing onto the positive plate of a capacitor than is flowing off the
negative plate. In that case the field in the neighboring wires contributed
by the capacitor, just outside the capacitor, is no longer the tiny fringe
field of a device with zero net charge. Now field in the wires can be
large, because the capacitor has a nonzero net charge, in this case a
positive net charge. What will this large field do? It will slow down the
conventional current approaching the positive plate, and it will increase
the conventional current leaving the negative plate. There is a built-in
feedback mechanism that will bring the two currents back to being equal.

That's a good description of the ideal situation. That describes
the way in which Kirchhoff's laws are enforced ... /assuming/ the
laws actually work.

That's fine as far as it goes, but in keeping with the spirit of
this thread, we should also consider the cases where Kirchhoff's
laws do not work.

In particular, suppose I grab a generic .1 μF capacitor from the
stockroom, and hook /both/ leads to a Van de Graaff generator.
Then /both/ capacitor plates will pick up a charge of the same
sign, and there will be no "feedback mechanism" to bring them
back to having equal-and-opposite charges.

Things get even weirder if I hook only /one/ of the leads to the
VdG generator, and leave the other lead floating, not grounded.

At this point conventional terminology fails us. Talking about
the «charge» on the capacitor is annoyingly ambiguous. To solve
this problem, I recommend introducing the term /gorge/. When a
capacitor has +q on one plate and -q on the other plate, we say
it has a /gorge/ equal to q. Specifically, we define the gorge
to be

G := (q1 - q2) / q
while -- as always -- the honest-to-goodness charge is
Q := (q1 + q2)

To describe a capacitor (or a battery) in situations where Kirchhoff's
law has failed, you need to specify both the gorge and the charge.
Note that according to the laws of physics, charge is strictly
conserved ... whereas gorge is not conserved. A battery can
disgorge itself via internal leakage processes.

For more discussion, including diagrams, see
http://www.av8n.com/physics/electrophorus.htm#sec-gorge