In the Debye–Hückel approximation, we maintain the system in thermodynamic equilibrium, at a temperature T high enough that the fluid particles obey Maxwell–Boltzmann statistics. At each point in space, the density of electrons with energy j has the form ρ ρ j ( r ) = ρ ρ j ( 0 ) ( r ) exp ⁡ ⁡ [ e ϕ ϕ ( r ) k B T ] where k B is the Boltzmann constant. Perturbing in φ and expanding the exponential to first order, we obtain e Δ Δ ρ ρ ≃ ≃ ε ε 0 k 0 2 Δ Δ ϕ ϕ where k 0 = d e f ρ ρ e 2 ε ε 0 k B T