the force. Because the charges alternate in sign, the series between conducting spheres of arbitrary radius and spac. The problem of the attractive force between unlike g does converge for all d> 2a ges is tackled in the same way. The charges q? appear at the same positions and with the same magnitudes but David nick, Fundamentals of Physics(Wiley, this time are all of one sign, negative on one side and posi- New York, 1986), 2nd ed, p. 457. Most elementary texts have a similar statement. tive on the other The resulting total force between the 2 Charles-Augustin Coulomb, "Law of electric force, "Mem.Acad.R charge systems is slightly larger than a-/d but, unlike the repulsive case, begins to diverge rapidly as d-2a In Fig. I 'William francis Magie, A Source Book in Physics(McGrawHill, New are plotted the logarithms of the repulsive, the a/d2, and York, 1935), p.408 the attractive forces as a function of the logarithm of the Coulombs many papers were reprinted in 1884 by Gauthier-Villars parameter /a Ofcourse, the a/d graph is a straight line. under the auspices of the Societe Francaise de Physique. This is the The distribution of image charges in a typical example is version that is most commonly available in American libraries. In the shown in Fig. 5 reprinted version of the 1785 papers on the electrostatic force there are The calculation of electric potentials, fields, and charge insertions in which the various assumptions of Coulomb are ana- distributions by the method of images is described in many yzed mathematically. In the first of these, the annotator calls attention undergraduate and graduate electricity texts. Smythe's to the small error due to coulomb s failure to account for inductive text is particularly useful because it was written after the GAbriel G. Luther and william r. Towler,"Redetermination of th possibly tedious calculations feasible. Smythe, for example,(1982 shows that the image charges for two conducting spheres Cf, for example, the discussion in Franklin Miller, college Physics(Har- satisfy a difference equation that can be solved in closed court Brace Jovanovich, New York, 1972), 3rd ed, p. 372 form: 7 Reference 6 q,=R,R2 sinh a/R, sinh na +R, sinh(n-1 sCf. Wolfgang K. H. Panofsky and Melba Phillips, Classical Electricity and Magnetism(Addison-Wesley, Reading, MA, 1955), p. 85 with mundT. Whittaker and George N. Watson, A Course of Moder (Cambridge U P, London, 1963), p. 382 Panofsky and Phill nian hs a=cosh-(d2-Ri-R2/2R, R 2 that the potential of the disk is We have chosen to present our calculations in computer v(a)=mEa x Jo,(x)sin x dx. iterative form simply because the interesting questions of physics and of mathematics(convergence, divergence)are okisl whittaker and Watson show that S.x- Jo(xrsin x dx=r/2,for more transparent in that form. Either method can be used William R. Smythe, Static and Dynamic Electricity(McGraw-Hill,New to calculate the potentials, forces, and capacitances York, 1968), 3rd ed, pp.128-131 1199 Am J Phys., Vol 58, No. 12, December 1990 Jack A Soules 1199