  In the present paper, dynamics of generalized charged particles are studied
in the presence of external electromagnetic interactions. This particular
extension of the free relativistic particle model lives in Non-Commutative
$\kappa$-Minkowski space-time, compatible with Doubly Special Relativity, that
is motivated to describe Quantum Gravity effects. Furthermore we have also
considered the electromagnetic field to be dynamical and have derived the
modified forms of Lienard-Wiechert like potentials for these extended charged
particle models. In all the above cases we exploit the new and extended form of
$\kappa$-Minkowski algebra where electromagnetic effects are incorporated in
the lowest order, in the Dirac framework of Hamiltonian constraint analysis.
