Irrotational Components of Maxwell?s Equations
David M. Drury
Maxwell?s equations separate into two sets of equations, one containing the solenoidal field components and the other containing the irrotational components. The solenoidal components of the electric and magnetic fields are shown to be produced by current densities, and contribute to electromagnetic radiation at speed in free space. The irrotational component of the electric field is produced by charge densities and propagates at infinite speed. Wave equations for the potential fields are derived with the Coulomb gauge, which gives simpler results than the Lorentz gauge. The scalar potential propagates at infinite speed while the vector potential propagates at speed c in free space. These results extend recent work by Oleinik on the electric field to the magnetic, scalar potential, and vector potential fields.
