Chapter 2 Multipole Expansion of the Electrostatic Potential

  • Published 2017


The potential of a localized charge distribution at large distance can be expanded as a series of multipole terms.1 The terms of the series depend on the charge spatial distribution in the system and have different dependence from the distance. In this chapter we will first examine the electric dipole, the simplest system after the point charge. We will write the dipole potential and obtain the expressions of the electrostatic energy, the force and the torque acting on the dipole in an external field. Then we will derive the first terms of the multipole expansion for the potential from a charge distribution. Finally we will write the general expression for the multipole expansion together the formula for the expansion in terms of spherical harmonics.

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@inproceedings{2017Chapter2M, title={Chapter 2 Multipole Expansion of the Electrostatic Potential}, author={}, year={2017} }