Image charges in metals

The total electrostatic potential in front of the substrate is given by the sum of the potentials caused by the ori nal charge (g ) phis that due to its image 

The second group of images has the same charge as the original one that is, Qi = Qi- These images are located at 

Consider now N particles confined to a slit-pore with metallic substrate surfaces. The total configurational potential energy of this system is then obtained from 

Finally, if the central cell comprising N particles is replicated along the x-and y- directions, we obtain a slab-like system confined between conducting walls. Introducing now three-dimensional lattice vectors 

The lattice sums in Eq. (6.65) reflect the fact that the Coulombic system between conducting walls has, in a way, three-dimensional periodicity. The basic cell of this three-dimensional array contains the original cell with the N particles plus the first set of images, that is, the N images resulting from the presence of just the lower wall [six Fig. 6.9(b)]. In fact, as we show explicitly in Appendix F.3.3, the energy of the extended system with a total of 2N charges, is directly linked to Uq by the relation 

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