# Point charge configuration with zero potential energy

1. Aug 16, 2012

### bigerst

is it possible to construct a system with only finite number of point charges of arbitrary magnitude at finite distance from each other such that the total potential energy is zero everywhere?
i doubt earnshaw's theorem would prohibit this construction, hence is it possible?
thanks

2. Aug 17, 2012

### Hassan2

If by potential energy , you mean the following integral:

$W=\int{\frac{1}{2}\epsilon E^{2}dv}$,

then zero total energy means zero electric field everywhere . Zero field around a point charge means zero net flux and this contradicts Gauss law.

3. Aug 18, 2012