Re: Surface charge distribution

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

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