Re: "Charged" capacitor mis-terminology

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

> We might want to remember that a number of our students will later be
> exposed to some part of the engineering world.  For those folks (as well
> as in older physics texts), there is a current between the plates a a
> capacitor (even one with "free space" between the planes).  The current of
> which they speak is the  DISPLACEMENT CURRENT .  Generally, they say that
> the current at any point in space is the sum of the CONDUCTION &
> DISPLACEMNET CURRENTS

>    I(total) = I(cond) + I(disp)

It's, not just old books and EE profs, but my students also get this 
terminology from me.

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

> It is, of course, a mathematical crutch so that the don't have to amend
> the naive form of Kirchhoff's 2nd rule/law.  If we would only teach the
> CONTINUITY EQUATION, we would have no need of I(disp).  The sum of the
> currents into or out of a junction need not be zero it there is a build-up
> of charge at that point.

It is only a mathematical crutch in so far as it is used to maintain the 
junction rule at the capacitor plate; and I introduce it this way, mostly as 
a hint of things to come when we study Faraday's law.  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.

> I usually find that if I take time to teach them only a little extra math
> (that they may not already know) I don't have to make up "virtual
> currents" to make Kirchhoff's Current Law work.

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

Joel