Re: Gauss' law and displacement current

["Carl E. Mungan" <mungan@USNA.EDU>]

I only read the digest, so my responses are considerably delayed. So
if you don't see comments on your posting it's because I haven't got
it yet. I have responded here to every single one I have seen, with
much thanks. Carl

> 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?

> These
> surface charges also source a field outside the wire.  ... The
> configuration of these charges changes when the switch is opened and the
> current ceases.

E_tangential is continuous so if there's a field in the wire, it
seems you're right that there must now be one just outside and that I
neglected that, good point. But that just seems to make the field
pointing into the Gaussian surface even bigger (more negative), so
that the flux in the two situations is even more different than I
thought.

> At any rate, constructing the Gaussian surface through the switch contacts
> helps show that the flux across the portion of the surface inside the
> original capacitor is not the only flux for this Gaussian surface.

Or equivalently that there is net charge on the enclosed switch
contact when the switch is open (since we now have two capacitors in
series) but not when it is closed. That's a very nice way to look at
things and might be the way to go! But meanwhile I'd like to pursue
the wire a little more if possible.

> I understand no current and no change of capacitor charge.  I understand
> current and a change of capacitor charge.  But I don't understand current
> and no change of capacitor charge.

Sorry for the poor explanations on my part. Take a snapshot of the
half charged capacitor with the switch open. Now remove charge dQ
from the capacitor, close the switch, and take a snapshot at the
instant dQ has flowed back onto the plate. Photographically subtract
the two photos to show where the charge and field configurations have
changed.

> *) Perhaps a diagram would help.

It sure would. In addition to or instead of the "subtraction photo"
above, I would like a diagram showing a portion of a long straight
wire joining a capacitor plate. Make a rough sketch of the locally
nonzero charges and of the electric field everywhere (ie. fields in
the wire, between the capacitor plates, and in the space outside of
the capacitor and wire; charges on the wire surface and on the
plate). I'd venture to guess someone can quickly draw something like
this by hand and scan it onto a webpage so we can all have something
to concretely discuss and refine.

>   -- In particular, if a wire is thin, it has only a small capacitance per
> unit length, so you can change its voltage with only a small amount of
> charge.   OTOH if you want to look closely there will be *some* charge
> involved.

Yes, this is exactly the kind of thing my original question was
after. Can we be a bit more specific about how this charge is
distributed?
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/