Re: funny capacitor (EUREKA ?)

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:37 AM 3/15/01 -0500, Bob Sciamanda wrote:

> if the electrical state of [the reference] point/object is influenced by
> my localized apparatus, then as my apparatus evolves in time, my gauge is
> a function of time.

OK, depending on how you set things up, that could happen.

> This will not invalidate the information in my voltmeter readings taken at
> any particular time,

Right.

> but would I have got some additional *time-dependent* information if I had
> chosen a zero reference point whose electrical state is unaffected by my
> apparatus?

No.

1) The topic of electrostatics exists only as a limit, in which the
lengthscale lambda is short and the timescale tau is long, so that
lambda/tau is small compared to the speed of light.  We need not require
lambda/tau to be zero, just small.

So for electrostatics, we must restrict the discussion to _slowly_ varying
potentials, charges, et cetera.  We can do that.  No problem.  The gauge,
whether it is time dependent or otherwise, does not interfere with our
ability to calculate and measure the slowly varying potentials, charges, et
cetera.

2) If we want to move beyond the electrostatic limit, to full-blown
electromagnetism, it becomes slightly tricky even to define what one means
by "electric potential".  You have to be careful, because there are
non-potential voltages running around.  And of course electricity is
related to magnetism, so you can't fool with the electric gauge unless you
do the "right" things with the magnetic gauge.

One way (not the only way) to do this is the "Lorentz gauge" ... see e.g.
  http://www.cs.cmu.edu/~jcl/classnotes/physics/classical_physics/maxwells_
http://www.cs.cmu.edu/~jcl/classnotes/physics/classical_physics/maxwells_equ
ations/maxwells_equations.html

but the bottom line remains:  no, it doesn't cause a problem to have the
electric gauge depend on time.