Re: whatever

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 15 Dec 1998, Dr. William Newbolt wrote:

> I remember reading that the displacement current between the plates of a
> charging capacitor is a convenient way to taking into account the fields
> due to charges running out onto the plates to charge the capacitor.  It
> was stated that one may use the displacement current or the currents in
> the plates, but not both for the calculations {of the magnetic field}.
> Is this the case?  Can anybody explain it to me?  Is it in J.  D.
> Jackson or any of the standard E & M books?  I haven't been able to find
> it!

I guarantee that you'll find it in any standard E & M book.  Ampere's law
is one of "Maxwell's equations and it relates the integral of the
tangential component of the magnetic field around any closed path to the
total flux of conventional current density (j) and displacement current
density (epsilon_o dE/dt) through any open surface spanning the chosen
path.

A standard conceptual example involves considering a small circular path
centered on a long wire carrying current to a capacitor somewhere down the
wire.  If one chooses the most obvious spanning surface--the one in the
plane of the circular path which slices through the wire--then there is
(almost) no displacement current, only conventional current.  If one
distorts the surface so that it runs through the region between the
capacitor plates without crossing any wires or capacitor plates, then
there is no conventional current, only displacement current.  One can also
choose paths that cut through the capacitor plates themselves picking up
some conventional current and some displacement current.  A detailed look
at this situation shows that all charge flowing onto the plates is counted
either directly as a part of the conventional current or indirectly due to
the additional electric field that it creates.

In any event there can be no ambiguity about what counts and what doesn't
count as long as you clearly specify the surface that you are considering.

John
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