Re: Gauss' law and displacement current

["John S. Denker" <jsd@MONMOUTH.COM>]

After disproving the notion that the current in a wire must be "sourced" by
surface charges on the wire, I remarked:

> > Make the loop polygonal (piecewise straight) if straightness is important
> > to you.  The same argument applies.

Then at 10:46 PM 4/23/01 -0400, Bob Sciamanda wrote:

> If (as I think you are proposing) the E field accompanying the changing
> magnetic flux is everywhere azimuthal ("circular") in direction,

That's not what I was proposing, but we can discuss it anyway....

> it will drive charge carriers into the sides of any straight wire.  A
> static surface charge will build up so that the NET field drives the
> current along the straight wire.

OK, in this case (where the shape of loop is slightly mismatched to the
shape of the electric field pattern) we find that
 a) the overall impetus for the current comes from a field that is _not_
due to any charges on the wire, while
 b) local steering of the current _is_ provided by surface charges

=======

It was never my intention to prove the extreme notion there is "no such
thing as surface charge on a wire".  Rather, my intention was to disprove
by way of counterexample the opposite extreme notion, namely the alleged
rule that
> > > the field inside the current carrying wire is
> > > sourced by surface charges on the wire.

For such a disproof, one counterexample suffices.  The counterexample need
not represent the general case.

The general case, obviously, lies somewhere between those extremes.
 -- Some electric fields are "sourced" by charges.  There's a term in
Maxwell's equations for that.
 -- Some electric fields are "sourced" by changing magnetic
fluxes.  There's a term in Maxwell's equations for that, too.

===========================

Finally:  I stand by my assertion that you _can_ have a wire with a long
straight section where there is a current but no surface charges, if that's
what you want.  You just need to drop the assumption that the changing flux
produces a "circular" field.  A non-circular distribution of time-varying
flux produces a non-circular field pattern.

The simplest way to construct the appropriate flux pattern in this case
would be to use a _bifilar transformer_ ... That is, a transformer where
the primary winding lies right next to the secondary winding.

The correctness of this construction should be obvious by symmetry.