- Explicit Examples of Free-Space Non-Planar Electromagnetic Waves Containing Magnetic Scalar Potentials (2000) [Updated 1 decade ago]
- Magnetic Potentials, Longitudinal Currents, and Magnetic Properties of Vacuum: All Implicit in Maxwell?s Equations (1997) [Updated 9 years ago]

- Explicit Examples of Free-Space Non-Planar Electromagnetic Waves Containing Magnetic Scalar Potentials (2000) [Updated 1 decade ago]
Electromagnetic waves (EMW) are formed by electric and magnetic fields, both together solution of Maxwell?s equations. The magnetic field is solenoidal always, while the electric field is solenoidal in charge-neutral regions only. Hence, conventionally, free-space electromagnetic fields are transverse to the direction of propagation; also, there exists a electric scalar potential but not a magnetic companion. Contrarywise, for the same homogeneous case, we exhibit explicit examples to show that: (a) Longitudinal magnetic fields are compatible with linearly polarized non-planar EMW, and (b) Magnetic scalar potentials are compatible with EMW. The direction of propagation of non-planar EMW oscillates around the direction of propagation of the plane EMW.

- Magnetic Potentials, Longitudinal Currents, and Magnetic
Properties of Vacuum: All Implicit in Maxwell?s Equations (1997) [Updated 9 years ago]
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.