Point charge configuration with zero potential energy

[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

 

[Hassan2]

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?

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.

 

[bigerst]

thanks for the reply.
i think that integral only apply to continuous charge distributions? doesn't 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