Cylindrical multipole expansion of electrostatic potential in form of triple sum of associated Legendre polynomials

Abstract

We present multipole expansion of electrostatic potential in cylindrical coordinates which contains triple summation in terms of associated Legendre polynomials. Multipole moments of presented expansion depend only on charge distribution and can be easily calculated analytically for cylindrically symmetric and other charge distributions with simple representation in cylindrical coordinates. Presented multipole expansion is employed in order to calculate potential of uniformly charged solid cylinder. Correctness of derived multipole expansion is verified by comparing multipole expansion of potential produced by uniformly charged solid cylinder with known expression for potential on its axis.