I Does Zero Potential at a Point Imply Zero Charge Density?

[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?

 

[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 $\alpha$.