Demonstrates the derivation of electrostatic potential and field from a charged sphere using spherical harmonics, suggesting an efficient mathematical approach.
The electrostatic potential and field produced throughout space by a charged spherical surface are derived by employing the spherical harmonics expansion of 1/|r-r'|, a term proportional to the Green function of the three-dimensional Laplacian. Once the potential is determined, the electric field is obtained by taking its negative gradient. This approach provides an efficient alternative to direct evaluation of the potential integral.
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Diego Valenzuela Castro (2026) studied this question.
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