Electrostatic internal energy using the method of images

Abstract

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

Modeling the Self-Assembly of Colloidal Nanorod Superlattices

“…The last coupling is realized through image charges, 16 where V i I is the coupling energy between the dipoles of the ith NR with all the mirrored dipoles. 46 The last term in eq 13 accounts for the coupling of the NRs to the electric field in the medium, given by eq 9. When we calculate the total energies of different NR superlattices from eq 13, we keep the NRs at fixed separations of d ) 2 nm.…”

“…The V surf potential energy is formed by the vdW coupling () or () and Coulombic coupling to the electrically conducting substrate. The last coupling is realized through image charges, where V i I is the coupling energy between the dipoles of the i th NR with all the mirrored dipoles . The last term in eq accounts for the coupling of the NRs to the electric field in the medium, given by eq .…”