Show that the total Coulomb self-energy of a sphereof radius R containing a charge Ze

Chapter 12, Problem 61

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Show that the total Coulomb self-energy of a sphereof radius R containing a charge Ze evenly spreadthroughout the sphere is given byECoul 351Ze224pP0R (12.17) Hint: Calculate the work done to bring a charge frominfi nity into a spherical shell of radius r and then integratethe spherical shell from 0 to R.

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