Re: "Charged" capacitor mis-terminology

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

In defending 'displacement current' as a *current* Joel wrote:
> I think it boils down to this: does a flux of something necessarily  involve 
> the flow of a corporal entity through a surface?  I interpret what David 
> says as implying "yes"; and I take the opposite viewpoint.  I gather from I 
> read below that David objects to my using the same term for flux of 
> something that is non-corporal that has been used for a flux of corporal 
> entities, i.e. "current".  Unless I misread what he wrote, that is the crux 
> of disagreement.

I don't mind the use of the term 'flux'.  It's the use of the term
'current' that I mind. Maybe I'm too fussy?

> Is displacement current a current of anything?; yes, its a current of 
> changing electric flux; which happens not to be corporal, but so what.  And 
> calling it a current I believe to be quite appropriate, because it produces 
> physically observable effects in the same fashion as conduction current.

The physical effects produced by 'displacement current', although
admittedly real, are not quite "in the same fashion as conduction
current".  The only similarity is that both of them, written as 3-space
vectors, seem to formally act as sources for a non-longitudinal magnetic
field.  In fact, it is the curl of the magnetic field minus the time
derivative of the electric field (aka the negative of the displacement
current subtracted from the source side of Ampere's equation) that
together form 3 spatial components of a single 4-tensor expression (in
Minkowski space) whose source-like term is the real electric current.
(BTW, the 4-th time-component of the tensor expression mentioned here is
just Coulomb's law relating the divergence of the E-field to the charge
density.)  Another way in which we can see that the 'displacement
current''s physical effects are different than those of real current is
that a real current of some stuff obeys (in a differential form) a
generalized continuity equation.  If j (vector) is the flux current of
some stuff whose density is [rho] then we should have:
d[rho]/dt + div(j) = C, where d/dt here is a partial derivative and C
represents the local rate of creation of the stuff per unit volume in
in space.  The meaning of the equation is that in any local region of
space the time rate of accumulation of stuff plus the net rate of stuff
leaving the region through the region's boundaries (i.e. *current* of
that stuff) is equal to the total net rate of creation of stuff inside
that region.  The stuff does not have to be 'corporal' to use Joel's
term.  If the stuff is nonconserved like entropy (when the process is
dissipative) then the creation term C is nonzero. If the stuff is
conserved like energy, electric charge, lepton number, probability,
momentum, etc. then the C term vanishs.  The essential idea for a
current is that it is the rate of flow of some kind of (whether tangible
or not) stuff that is subject to quantitative measure and needs to be
accounted for.  The 'displacement current' does not obey such a
generalized continuity equation.  In fact, the supposed 'displacement
current' actually gives, in a hidden form, the d[rho]/dt term in the
continuity equation for the real electric charge (stuff).

> ...
> I'd say why not?; it gave whoever came up with the term "displacement 
> current" the license to call that  a current.  I'd have no trouble talking 
> about a magnetic displacement current.
 
I think it was Maxwell who first called it a current.  Einstein also
named 'relativistic mass'.  I don't think it's a good idea to use that
terminology either.  But, please, let's not get off on that one again.
Sometimes, when a theory is being formulated for the first time, its
inventor may refer to some aspect of the theory by a name that, after
subsequent refinement, mathematization, and history of use, it becomes
clear that a better way of referring to that aspect exists (or ought to
be constructed).

But when all is said and done, if you like the term 'current' and its 
associated connotations for the 'displacement current' term in Ampere's
law, I certainly can't stop you from using it.  I wouldn't even add it
to Ludwik's list of textbook misconceptions.  My only quarrel with the
use of the term 'current' for this flux is that it may tend to suggest
some conceptual things to the unsuspecting student that are not the case.

David Bowman
dbowman@gtc.georgetown.ky.us