Linearized planar screening solution ($\psi =\zeta e^{-\kappa x}$)

For $|e\psi |\ll k_{B}T$, $\psi \prime \prime ={\kappa }^2\psi$ with ${\kappa }^2=2e^2{n}_0/(\epsilon k_{B}T)$ for a symmetric monovalent salt with per-species reservoir density $n_0$. The half-space solution with $\psi (0)=\zeta$ and vanishing bulk potential is $\zeta e^{-\kappa x}$. If density denotes the sum of species, the written factor of two changes.