Re: Surface charge distribution

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Jack Uretsky wrote:

>         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.

Which, in turn, means that they arrange themselves so that the
electric field is zero everywhere within the conducting material
itself.

> This requires that the positive charges all get pulled to the inner
> surface,

("all"?  What does that mean?)

> 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.

On the contrary; uniformity will *insure* that currents exist (as a
result of the superposed nonspherically symmetric field of the off
center charge.)  Those currents will end when the appropriate
*nonuniform* distribution arises (on the inner surface only as it
turns out) as a direct result of those currents.

>         Note that a spherical Gaussian surface that lies completely within
> the shell (that is, between the inner and outer surfaces of the shell) is
> in a field-free region.  The net charge enclosed is zero.

This is true for *any* Gaussian surface--spherical or not--that lies
in that region.

>         A similar surface outside of the outer surface of the shell must
> then enclose a net charge equal to the charge that was place inside (of
> the inner surface) of the shell.

Of course.

--
   A. John Mallinckrodt        http://www.csupomona.edu/~ajm
   Professor of Physics      mailto:ajm@csupomona.edu
   Physics Department         voice:909-869-4054
   Cal Poly Pomona              fax:909-869-5090
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