# In a region free of charges, an external charge can not be in stable equilibrium

How to prove using Gauss' theorem that in a region free of charges, an external charge can not be in stable equilibrium due to electrostatics forces alone ?

I tried like this: Using Gauss' law divergence of electric field is zero. How do I connect the idea of stable equilibrium with this ? How can there be external force on the test charge when there is no source charge ?

-
 it is called Earnshaw's theorem (en.wikipedia.org/wiki/Earnshaw%27s_theorem) – Yrogirg Aug 30 '12 at 7:07