Using the Coulomb gauge where ∇ ∇ ⋅ ⋅ A = 0 and V = 0 , the vector potential of light is given by A = A 0 ε ε e i ( q ⋅ ⋅ r − − ω ω t ) + C where the resulting electric field is E = − − ∂ ∂ A ∂ ∂ t = i ω ω A 0 ε ε e i . ( q ⋅ ⋅ r − − ω ω t ) .