Electrostatic internal energy using the method of images

摘要

For several configurations of charges in the presence of conductors, themethod of images permits us to obtain some observables associated with such aconfiguration by replacing the conductors with some image charges. However,simple inspection shows that the potential energy associated with both systemsdoes not coincide. Nevertheless, it can be shown that for a system of agrounded or neutral conductor and a distribution of charges outside, theexternal potential energy associated with the real charge distribution embeddedin the field generated by the set of image charges is twice the value of theinternal potential energy associated with the original system. This assertionis valid for any size and shape of the conductor, and regardless of theconfiguration of images required. In addition, even in the case in which theconductor is not grounded nor neutral, it is still possible to calculate theinternal potential energy of the original configuration through the method ofimages. These results show that the method of images could also be useful forcalculations of the internal potential energy of the original system.