  We calculate the electrostatic self-force on an electric dipole in the
spacetime generated by a static, thin, infinite and straight cosmic string. The
electric dipole is held fixed in different configurations, namely, parallel,
perpendicular to the cosmic string and oriented along the azimuthal direction
around this topological defect, which is stretched along the z axis. We show
that the self-force is equivalent to an interaction of the electric dipole with
an effective dipole moment which depends on the linear mass density of the
cosmic string and on the configuration. The plots of the self-forces as
functions of the parameter which determines the angular deficit of the cosmic
string are shown for those different configurations.
