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Regarding Bill Beaty's appeal to displacement current to understand
current continuity:

If "displacement current" is allowed into our explanation, then we are
able to say that electric currents can only exist in loops. Even when
charge flows in a single wire between two oppositely-charged, isolated
objects, there must be a corresponding displacement current in the space
surrounding the objects, directed oppositely to the charge-flow in the
wire.

This is backwards or, at least, misleading. It is the presence of the
so-called 'displacement current' term in Ampere's law that *permits*
localized charge imbalances to exist such that the current into a given
region of space does not have to necessarily equal the current out of that
region. The 'displacement current' term is what allows us to conclude that
the difference between the current into a region of space and the current
out of that region is the net rate of accumulation of charge inside that
region. If one dropped the 'displacement current' from Ampere's law we
would have to conclude that the current flux is everywhere locally
divergence-free. (This is because the divergence of the curl of the
magnetic field is automatically zero.) A divergence-free flux of current
is merely a differential statement of Kirchoff's current law, (i.e. the
net current into a region of space is zero). It is the presence of the
'displacement current' term that allows Kirchoff's current law to
break down into the usual continuity law expressing the conservation of
charge--yet allowing localized charge imbalances to develop (such as on
individual capacitor plates) and subsequently to neutralize. Contrary
to the seeming connotation of its name, 'displacement current' is *not* a
special form of any actual kind of current.

However, that being said, if we want to "save the appearances" of
Kirchoff's current law it can be done in a way that I think that Bill was
alluding to. If we, by fiat, write the sum of the actual current and the
'displacement current' as a kind of "effective current", then this
"effective current" *does* obey Kirchoff's current law and the flux of this
"effective current" is divergence-free, meaning that its streamlines always
form loops. It should be emphasized, though, that this is only a
mathematical trick which lets us think of the rate of localized charge
accumulation as a sort of effective flux current which only works because
the local charge density happens to be a divergence (of the electric
field).

BTW, not only does 'displacement current' in Ampere's law cause the
breakdown of Kirchoff's current law for nodes, but the induction term in
Faraday's law causes the breakdown of Kirchoff's voltage law for loops.
Without Faraday's induction term the electric field would be everywhere
curl-free. This would imply the existence of a 'scalar' potential field
whose (negative) gradient is everywhere the electric field. This would
result in the sum of the potential drops around any closed loop (i.e. the
net EMF around any closed loop) to always vanish. In both cases
(Faraday induction, and 'displacement current') it is precisely these
terms which introduce explicit time dependence into electromagnetism and
which couple, otherwise separated, magnetostatics (whose sources are static
current distributions) and electrostatics (whose sources are static charge
distributions) together to make electromagnetism.

David Bowman
dbowman@gtc.georgetown.ky.us