  After having obtained previously an extended first approximation of Maxwell's
equations in Fock's nonlinear relativity, we propose here the corresponding
exact form. In order to achieve this goal, we were inspired mainly by the
special relativistic version of Feynman's proof from which we constructed a
formal approach more adapted to the noncommutative algebra. This reasoning lets
us establish the exact form of the generalized first group of Maxwell's
equations. To deduce the second one, we have imposed the electric-magnetic
duality. As in the k-Minkowski space-time, the generalized Lorentz force
depends on the mass of the particle. After having restored the R-Lorentz
algebra symmetry, we have used the perturbative treatment to find the exact
form of the generalized Dirac's magnetic monopole in our context. As
consequence, the Universe could locally contain the magnetic charge but in its
totality it is still neutral.
