A plasmaPlasma is a spatial distribution of charges which are in thermal equilibrium or steady state with one another. Examples include the ions in an electrolyte solutionElectrolyte solution, and the ions and electrons in a steady state electric discharge. In a plasma, charges of opposite sign tend to drift toward one another under the action of their mutual electric fields. If this were the sole force acting, the oppositely charged ions would recombine and the spatial distribution of charges would collapse. As realized by Debye, however, the drift of charges of opposite signs towards one another increases the local charge density. As the second law of thermodynamics favors a uniform distribution of charge, the local increase in charge density adjusts by partially diffusing back into the surrounding material. The result is an equilibrium charge distribution in which each charge is surrounded by a radially decreasing atmosphere of opposite charge. Consistent with the charge neutrality condition, the integral of the charge distribution over the entire sample is zero. The determination of the electrostatic potential requires a method of solution of the Poisson equation which maintains self-consistency. This is achieved by setting the potential of mean force acting on a given ion equal to the charge on the ion times the electrostatic potential evaluated at the position of the ion. The result is the so-called Poisson–Boltzmann equationPoisson–Boltzmann equation. In this chapter, we use the Poisson-Boltzmann equation to solve for the electrostatic potential in the case of a charged flat plate dipped in an electrolyte solutionElectrolyte solution. The result is subsequently used to calculate the electrostatic force of repulsion between two like charged parallel plates. This case is relevant to the problem of colloidal charged particle coagulation. In another example, we solve the Poisson–Boltzmann equationPoisson–Boltzmann equation in cylindrical polar coordinates for the case of a charged rod in an electrolyte solution. This result improves upon the single rod model for a charged DNA strand considered in Chap.  1 .