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    Green's Function and Spherical Harmonics

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

    © BrainMass Inc. brainmass.com October 10, 2019, 7:46 am ad1c9bdddf
    https://brainmass.com/physics/electricity-magnetism/greens-function-potential-spherical-harmonics-expansion-594331

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    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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