Earnshaw's theorem
= Earnshaw's theorem
{c}
{wiki}
For a point <electric charge> in a charge-free neighbourhood, a static <electric potential> obeys <Laplace's equation>. The <maximum principle for harmonic functions> excludes a strict interior minimum or maximum of that <electric potential>, hence a strict minimum of the charge's <potential energy>. A static <electric field> alone therefore cannot provide stable three-dimensional confinement under these assumptions.