  This scientific essay proposes to discuss the physical aspects of a system
consisting of some non-relativistic massive charged particles, that are the
sources in motion of an electromagnetic field (e.m.) propagating through the
space, filled by a linear, homogeneous, and isotropic material medium. The
physical link between the conservation of total momentum and the solenoidality
of a magnetic induction field is investigated. After a careful review of all
the more widely sustained didactic justifications for the solenoidality of
magnetic induction, some properties of the Maxwell e.m. stress tensor are
defined according to Minkowski. This study presents a new framework wherein the
necessary condition for the free-divergence of magnetic induction in the entire
space, here named as solenoidality condition, derives directly from the total
momentum conservation of the system, i.e. particles plus field. The theoretical
treatise generally leads to results that leave some open questions on the
existence, or at least the observability, of the magnetic monopoles. Their
observability is theoretically plausible only under suitable assumptions of
symmetry that, in the opinion of authors, may be in any case an interesting
topic of scientific discussion especially in the field of experimental physics.
