1. Dec 20, 2011

### N2O2

1. The problem statement, all variables and given/known data

I want to prove that coefficients of potential are non-negative. i.e. Pij ≥ 0

2. Relevant equations

By coefficients of potential method we know that in a system of conductors the potential on ith conductor is related to charges on conductors by:

$\Phi$i = $\sum$ Pij Qj

3. The attempt at a solution

It is written in Reitz and Milford that it is hard to prove in a rigorous way. I think that we should use Pii ≥ Pij.

2. Dec 20, 2011

### ardie

how is the system arranged?

3. Dec 21, 2011

### N2O2

This is a general statement. Of course we should set a specific arrangement to obtain a result. for example put Qi on ith conductor and assume jth conductor to be grounded and Q on other conductors to be zero.
But I haven't found the correct conditions.

4. Dec 21, 2011

### ardie

in your scenario, should the conductors be sufficiently a long way away, their potentials will not effect each other (to a certain approximation) hence defeating the equation connecting the potential of one to the charge of another.