To apply these, the polarizations need to be defined so that the form of the Hertz vectors can be obtained. Considering the case of simple electric polarization provides the path to finding this form via the wave equation. Assuming the space is uniform and non-conducting, and the charge and current distributions are given by ρ ρ ( r , t ) , J ( r , t ) , define a vector P = P ( r , t ) such that ρ ρ = − − ∇ ∇ ⋅ ⋅ P and J = ∂ ∂ P ∂ ∂ t . Using these to solve for the Π Π vectors is similar to how the auxiliary fields D and H can be found, however here the Hertz vectors treat the electric and magnetic polarizations as sources. The Hertz vector potentials from these sources, Π Π e for the electric Hertz potential, and Π Π m for the magnetic Hertz potential can be derived using the wave equation for each.