Re: Surface charge distribution

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Chuck Britton wrote:

> Is the conducting shell specified as being SPHERICAL ?!?!?!?!?!

This *is* an important point.

> If yes - then yes, since the shell is conducting,  - the E field is
> uniform around it and Gauss's Law tells us that the charge
> distribution is symmetric.

It seems to me that there is a missing piece of logic here akin to
the "chicken and egg" problem

Gauss's law does tell us that a spherically symmetric exterior field
implies a spherically symmetric charge distribution on the outer
surface, but how do we *know* that the exterior field is spherically
symmetric?

The easy way to prove it is simply to invoke the existence-uniqueness
property of solutions to Laplace's equation:  Since we have found *a*
solution to this problem that satisfies all boundary conditions and
that includes a spherically symmetric exterior field, it is *the*
solution to the problem.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm