The electric field in terms of the Hertz vectors is given as E = ∇ ∇ × × ∇ ∇ × × π π e − − P ϵ ϵ 0 − − ∂ ∂ ∂ ∂ t ( ∇ ∇ × × π π m ) , but the magnetic Hertz vector π π m is 0 since the material is assumed to be non-magnetizable and there is no external magnetic field. Therefore the electric field simplifies to E = ∇ ∇ × × ∇ ∇ × × π π e − − P ϵ ϵ 0 .