On the difference between the charge-free and the charge-neutral solutions of Maxwell equations

Abstract

It is conventionally believed that solutions of so called "free" Maxwell equations for \varrho=0 (density of charge) describe the free electromagnetic field in empty space (if one considers the free field as a field, whose flux lines neither begin nor end in a charge). We consider three types of regions: (i) "isolated charge-free" region (where all electric fields, generated by charges outside that particular region, are zero), for example, inside a hollow conductor of any shape or in a free-charge Universe; (ii) ``non-isolated charge-free" region (where all electric fields, generated by charges outside that particular region, are not zero) and (iii) "charge-neutral" region (where point charges exist but their algebraic sum is zero). The paper notes that there are two families of solutions: (1) In "isolated charge-free" regions electric free field does not exist in the context of Maxwell's equations, but there may exist a time-independent background magnetic field. (2) In both "charge-neutral" and "non-isolated charge-free" regions where the homogeneous condition \varrho=0 also holds, Maxwell's equation for electric field have non-zero solution, as in the conventional view, but this solution is not free field. We mention some implications related to free-electromagnetic fields and the simplest charge-neutral universe.