  Following the line of the history, if by one side the electromagnetic theory
was consolidated on the 19th century, the emergence of the special and the
general relativity theories on the 20th century opened possibilities of further
developments, with the search for the unification of the gravitation and the
electromagnetism on a single unified theory. Some attempts to the
geometrization of the electromagnetism emerged in this context, where these
first models resided strictly on a classical basis. Posteriorly, they were
followed by more complete and embracing quantum field theories. The present
work reconsiders the classical viewpoint, with the purpose of showing that at
first order of approximation the electromagnetism constitutes a geometric
structure aside other phenomena as gravitation, and that magnetic monopoles do
not exist at least up to this order of approximation. Even though being
limited, the model is consistent and offers the possibility of an experimental
test of validity.
