If a body becomes charged by losing electrons for example, it will experience a braking force when it is accelerated due to radiation called Bremsstrahlung radiation. Part of the energy used to accelerate the charged body will be emitted as radiation. It should therefore take more energy to accelerate the charged mass than the energy required to accelerate the body without the charge.
The Larmor formula calculates the non-relativistic power radiated by the acceleration. There is also a relativistic derivation.
The charged body will appear to be more massive due to this effect. It can be explained by the fact that part of the energy is going to kinetic energy and part to radiation. Nevertheless, F=ma should imply a higher mass so are we dealing with a more massive body?