The charge distribution on a conductor for non-Coulombic potentials

We study the distribution of charge on a conductor for Yukawa (e(-mur)/r) a nd power-law (1/r(n)) potentials. In the Yukawa case some charge goes to th e surface, while the remainder distributes uniformly over the volume. In th e power-law case no such general result is available, but we obtain the dis tribution for spheres, cylinders, and slabs, on the range 1 less than or eq ual to n less than or equal to 3 . In the Coulomb limit (n = 1) the charge all goes to the surface; at the other extreme (n = 3) it distributes unifor mly over the volume. (C) 2001 American Association of Physics Teachers.