We have recently obtained new explicit nonperiodic solutions for the three-dimensional timedependent wave equation in spherical coordinates. Since Maxwell field equation (MFE) is formed by four wave equations, our results also lead to nonperiodic solutions of the set of classical Maxwell?s equations (ME). To understand the meaning of these new expressions, we revisited the standard derivation of MFE from ME. Firstly, we reviewed the standard representation of magnetic and electric fields in terms of potentials to conclude that the magnetic scalar potential is as fundamental as the conventional electric scalar term. Next we checked the conditions for the equivalence of the classical and the field representations of ME to conclude that the class of Lorentz invariant inductive phenomena may contain nonvanishing longitudinal currents. This result agrees with Evans recent discovery of a longitudinal photomagneton. Finally, invariance under Lorentz gauge transformations leads to identifying a new constraint for the magnetic properties of the vacuum.
