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    Non-uniform Surface Charge Density

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    Please see the attached file.
    A spherical shell of radius R centered at the origin has a surface charge density (file attached).
    1. Setup the Coulomb integral for the electric potential V(z) for any point on the z axis. Find the function.
    2. Evaluate V(z) at the origin (z=0)

    Note: you may need to look up the integral.

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    Solution Summary

    The solution shows the potential at the center of a spherical shell with non-uniform surface charge density.