complications if no multipole expansion

[Jeroen Wouters]

The goal of the multipole expansion is to decompose a complex charge distribution into simpler scalar/vectorial quantities. You make it easy to work with the charge distribution. If you use perturbation theory before making the multipole expansion, you will run into the problem that you don’t have these simple expressions for the charge distribution. You don’t have the thing you want to apply the perturbation to. Furthermore, perturbation theory is meant for small corrections, not for a general expression.

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