# Green's Function and Spherical Harmonics

Please see the attached file. It is taken from "Classical Electrodynamic 3rd by Jackson".

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#### Solution Preview

We know that the Green's function for a sphere with Dirichlet's boundary conditiosn is

(1.1)

If the angle between and r is then it can be written as:

(1.2)

On the surface of the sphere:

(1.3)

The potential is given by:

(1.4)

Since there is no excess free charge we have

Since this is Green's function with ...

#### Solution Summary

This solution shows how Green's Function and the Spherical Harmonics Expansion are equivalent.

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