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We analyze the electrostatic self-energy of a point like electrically chargedparticle induced by a cosmic string in the context of gravity's rainbow, aswell the electrostatic self-force on this particle. The possibility of thesolution associated with a charged particle to be altered by modifications indispersion relations of the space-time is discussed. We show that theself-energy depends on the rainbow functions and that this quantity can eitherincrease or decrease depending on the rainbow function chosen, as compared withanalogous result in the framework of general relativity. With respect to theself-force, its dependence with the rainbow functions is also pointed out

Electrostatic self-interaction of charged particles in the space-time of a cosmic string in the context of gravity's rainbow