I Poissons equation basic question

1. Sep 24, 2016

aaaa202

Poissons equation for the electrostatic potential is:

2φ = -ρ/ε

My question is simple: If φ=0 at a point (x,y,z) can we then conclude also that ρ is zero at that point?

2. Sep 24, 2016

Fightfish

The value of the potential at a single point has no physical meaning - you can always arbitrarily shift it by a reference value.

More concretely, $\nabla^{2}\left(\varphi + \alpha\right) = \nabla^{2}\left(\varphi\right)$ for any constant $\alpha$.