  In this work, we explore the possibility that quantum fluctuations induce an
electric or magnetic charge or both, in the context of Gravity's Rainbow. A
semi-classical approach is adopted, where the graviton one-loop contribution to
a classical energy in a background spacetime is computed through a variational
approach with Gaussian trial wave functionals. The energy density of the
graviton one-loop contribution, in this context, acts as a source for the
electric/magnetic charge. The ultraviolet (UV) divergences, which arise
analyzing this procedure, are kept under control with the help of an
appropriate choice of the Rainbow's functions. In this way we avoid the
introduction of any regularization/renormalization scheme. A comparison with
the observed data lead us to determine the size of the electron and of the
magnetic monopole which appear to be of Planckian size. Both results seem to be
of the same order for a Schwarzschild and a de Sitter background, respectively.
Estimates on the magnetic monopole size have been done with the help of the
Dirac quantization procedure. We find that the monopole radius is larger than
the electron radius. Even in this case the ratio between the electric and
magnetic monopole radius appears to be of the same order for both geometries.
