Re: "Charged" capacitor mis-terminology

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

If John Ertel's comments on displacement current had showed up in my
mail box just a little sooner I wouldn't have posted my comments on the
subject because I agree with so much of what he said.  Unfortunately,
our posts have somehow crossed in the mail. BTW, I haven't seen my post
show up yet.  I guess the list is still hiccuping.  In any event I
wanted to respond to a couple of things that Joel Rauber said in
response to John's post.

> I see nothing wrong with your equation above, and it represents a 
> generalization of current from simply being charges in motion.

It is very much a generalization--so much so that it can be misleading.
Displacement current does not represent anything close to a current in 
the sense of its usual meaning as the rate of flow of some sort of
stuff.  (It's time for Leigh to chime in here about reification.)
Nothing flows in a displacement current.  Rather it is just a time rate
of change of the flux of electric field (or displacement field if one
is inclined to use that macroscopic notion).  I have never heard anyone
call the time rate of change of the flux of magnetic induction in
Faraday's law a 'magnetic displacement current' analogous to the
electric displacement current in Ampere's law--yet this term is just
what the symmetry of Maxwell's equations says it is.  There is a good
reason for this; nothing necessarily flows when a magnetic field changes
in a region of space.  It is true that a time-changing magnetic flux 
mathematically acts as a source for a non-longitudinal (non-irrotational,
maybe rotational?) electric field (EMF), but that doesn't give us license
to call it a current.  Since we do not regard a time-changing magnetic
flux as the flow of some kind of magnetic displacement current, then
neither should we regard a time-changing electric flux as the flow of some
kind of electric displacement current, even though it mathematically
acts as a source for a non-longitudinal magnetic field.

> ...                                                .  But Displacement 
> current is quite real, because it has manifestly physical effects.  It is a 
> source of real magnetic fields that have physically observable effects on 
> compass needles; Therefore it is not *only* and *purely* a mathematical 
> crutch.

It certainly does exist when an electric flux changes; its just not a
*current* of anything.  It is the pretending of it *as a current* that is
the mathematical crutch.

> Displacement current is not virtual and is not made up; it has physically 
> observable affects and consequences.

I doubt that John meant the word virtual as somehow unreal or ontologically
nonexistent (although I should let him speak for himself here).  I suspect
that he meant it only so far as its status functioning as a *current* is
concerned, not in terms of its status as what it actually is, namely, a
time rate of change of electric flux.

David Bowman
dbowman@gtc.georgetown.ky.us