Why does an accelerating neutral object not emit Bremsstrahlung radiation? It is a well established fact that accelerating charges, positive or negative, emit radiation. Why then does a neutral object made up of equal amounts of positive and negative charge not emit any radiation when accelerated?
 A: If the object has a net electric dipole (or quadrupole, or higher) moment, that indicates that the charge is not all located in the same place withing the body.  In that case, it will radiate a certain amount when it is accelerated (but less than an object with a nonzero net charge).
However, if the positive and negative charges are distributed in the same way, then there is no net radiation from the body (no electromagnetic field at all, in fact).  You can imagine two separate moving bodies, one positively charged and one negatively charged, following exactly the same trajectory; together, they make up the composite particle.  Either of the charged components on its own would radiate when it is accelerated.  However, the outgoing radiation from the positive and negative bodies are exactly the same, except for an overall sign difference between them; that means that the radiation between the positive and negative charges making up the body interfere destructively, leaving no net radiation.
Returning to the case of a neutral body with an electric dipole moment, the moving positive and negative charges again radiate, but since the source charges are not in exactly the same place, the outgoing waves have slightly different phases.  There is still a great deal of destructive interference, but the result is not perfect cancelation, and so there is a certain small amount of radiation emitted.
