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    The Potential of a Disk With a Certain Charge Distribution

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    Please see the attach file for the question taken from "Classical Electrodynamics 3rd by Jackson".

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    Solution Preview

    First, let's calculate the potential along the z-axis.
    The charge surface density is given by:
    Where K is some constant to be determined later.
    The potential along the z axis is given by (in polar coordinates):
    The angular integration just gives a factor of , so:

    This is a conducting disk, hence the potential over the disk is constant V, specificaly ...

    Solution Summary

    The solution shows in detail how to find the potential everywhere using Legendre expansion once we know the potential on the z axis.