When a substance gets polarized by an electric field, we can describe it by a polarization density p, which describes a dipole moment per unit volume. consider a thin cylindeir aligned along the z axis made of a dielectric. suppose there is an ambient electric field in the direction so that the dielectric has a uniform polarization density p = p2. consider a point o a distance r from the center of the cylinder, and a distance rı and r2 from the bottom and top of the cylinder (located at z1 and z2, respectively.) now, a segment of length dz along the cylinder corresponds to a volume dv-dzda, where da is the (small, constant) cross-sectional area of the cylinder. we then assign arn electric dipole moment p - p dv to this little volume. using the class result that the potential due to a dipole s v(r)rate along the cylinder to find the potential at point o, showing that it looks like the potential of a point charge p da at the top of the cylinder, combined with another of charge -p da at the bottom of the cylinder. (see fig. 1). note: if we were then to consider a slab of dielectric to be composed of many such columns this tells us precisely that the net effect of the polarized material is the same as two sheets of charge with surface charge density cos