Dimensional Analysis Poisson Equation

[aaaa202]

Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads

d²φ/dx² = ρ(x)/ε

Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?

 

[Orodruin]

Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads

d²φ/dx² = ρ(x)/ε

Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?

The potential is arbitrary. You can shift it by a constant and still satisfy the Poisson equation.