# 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

### bigerst

thanks for the reply.
i think that integral only apply to continuous charge distributions? doesnt it predict the energy of a point charge is infinite.
on another note i think i got the answer, apparently it is possible to assemble point charges such that they have no mechanical energy

bigerst

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