For a charge of magnitude z e (where e is the elementary charge) moving with velocity v , the density and charge density can be expressed as ρ ρ ( x → → , t ) = q δ δ ( x → → − − v → → t ) and J → → ( x → → , t ) = v → → ρ ρ ( x → → , t ) , taking the Fourier transform gives: ρ ρ ( k → → , ω ω ) = q 2 π π δ δ ( ω ω − − k → → ⋅ ⋅ v → → ) J → → ( k → → , ω ω ) = v → → ρ ρ ( k → → , ω ω )