Re: Gauss' law and displacement current

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

At 12:08 PM 4/23/01 -0400, Eugene Mosca wrote:
> >> For example, the field inside the
> >> current carrying wire is sourced by surface charges on the wire.
> >
> > Is this true even for portions of a very long, straight wire well
> > away from any corners?
>
> In a word, yes.  This is discussed in Chapter 6 of Chabay and Sherwood's
> "Electric & Magnetic Interactions," Wiley (1995).


I don't have that reference at hand, but I find the result to be highly
implausible.

In particular, consider a large _loop_ of wire.  Run some flux through the
middle of the loop.  (Consider the wire to be a one-turn short-circuit
secondary on a transformer if you like, and ramp up the current in the
primary.)

Then there will be a current in the wire.  By symmetry, it is exceedingly
hard to see how the field could be "sourced" by surface charges (or any
other kind of charges).

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