On the Divergenceless Property of the Magnetic Induction Field

Abstract

Maxwell's equations beautifully describe the electromagnetic fields properties. In what follows we will be interested in giving a new perspective to divergence-free Maxwell’s equations regarding the magnetic induction field: . To this end we will consider some physical aspects of a system consisting of massive nonrelativistic charged particles, as sources of an electromagnetic field (e.m.) propagating in free space. In particular the link between conservation of total momentum and divergence-free condition for the magnetic induction field will be deeply investigated. This study presents a new context in which the necessary condition for the divergence-free property of the magnetic induction field in the whole space, known as solenoidality condition, directly comes from the conservation of total momentum for the system, that is, sources and field. This work, in general, leads to results that leave some open questions on the existence, or at least the observability, of magnetic monopoles, theoretically plausible only under suitable symmetry assumptions as we will show.