The Nernst–Planck equation is a continuity equation for the time-dependent concentration  of a chemical species:
where  is the flux. It is assumed that the total flux is composed of three elements: diffusion, advection, and electromigration. This implies that the concentration is affected by an ionic concentration gradient , flow velocity , and an electric field :
where  is the diffusivity of the chemical species,  is the valence of ionic species,  is the elementary charge,  is the Boltzmann constant, and  is the absolute temperature. The electric field may be further decomposed as:
where  is the electric potential and  is the magnetic vector potential. Therefore, the Nernst–Planck equation is given by: