Re: Surface charge distribution

[Jack Uretsky <jlu@HEP.ANL.GOV>]

We agree that there must be no tangential field at any shell surface.  The
field lines inside are all normal to the surface.  So the charge cannot be
uniformaly distributed over the inner surface, because the field from the
induced charge could not cancel the tangential components of the
off-center charge.  By golly, you're right!

So it is important to go through the analysis step by step.
                        Thanks for reminding me.
                                                Jack
On Wed, 4 Dec 2002, Bob LaMontagne wrote:

> Jack Uretsky wrote:
>
> > Hi-
> >         The only response that I saw just gave an answer without an
> > explanation.  I suggest that the reverse would be a better practice.
> >         A charge is placed off-center inside a spherical conducting shell.
> > Find the field outside of the shell.
> >         The issue is: what is the meaning here of (perfectly) "conducting
> > shell"?
> >
> > What is meant is that that the positive and negative charges in the shell
> > are free to position themselves so that no currents flow in the shell.
> > This requires that the positive charges all get pulled to the inner
> > surface, the negative charges are pushed to the outer surface, and the
> > charges distribute themselves uniformly - that's the key, uniformly - over
> > each surface.  Uniformity is required to avoid currents running along the
> > surface.
>
> Jack - maybe just quibbling here, but the charges drawn to the inner surface
> certainly must have a non-uniform distribution if they are to cancel the field
> in the shell from the off-center charge in the cavity. They must be more dense
> where the field from the central charge is greater and less dense where it is
> less. Maybe I'm just misunderstanding your term "uniformly". If you simply
> mean smoothly varying then maybe we agree. The main point is that the charges
> in the shell rearrange until the fields cancel in the shell, hence no further
> motion of charges. The net field at the shell's surface must have no
> tangential components or else there will be surface currents. If the inner
> induced charges were uniform the off-center cavity charge would have
> tangential field components at the shell's inner surface.
>
> Bob at PC

--
        "What did Barrow's lectures contain?  Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings.  (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
                                        V. I. Arnol'd in
                                Huygens & Barrow, Newton & Hooke