  We consider the equation of motion of a charged particle or a charged compact
object in curved space-time, under the reaction of electromagnetic radiation
and also consider a physical situation such that the charged particle or
compact object emits gravitational radiation, thereby gravitational radiation
reaction also acts on it. We investigate the effect of this metric perturbation
i.e. the gravitational radiation on the electromagnetic self-force.
  We show that, besides the interaction terms derived by P. Zimmerman and E.
Poisson (Phys. Rev. D 90, 084030, 2014), additional perturbative terms are
generated, which are linear in metric perturbation and are generated due to
perturbation of the electromagnetic self-force by the metric perturbation. We
discuss the conditions of significance of these perturbative terms and also the
interaction terms with respect to the gravitational self-force in various
astrophysical and cosmological cases ; such as the motion of charged particles
around black holes, some extreme mass-ratio inspirals (EMRIs) involving
sufficiently accelerated motion of charged stars (specially neutron stars) or
charged stellar mass black holes around supermassive black holes, and motion of
charged particles around charged primordial black holes formed in the early
Universe etc.. We find that in some astrophysical and cosmological cases these
perturbative terms can have significant effect in comparison with the
gravitational radiation-reaction term.
