Electrostatic Potential and Field of a Charged Sphere: Spherical Harmonics Approach

Key Points

• The aim is to derive the electrostatic potential and field produced by a charged spherical surface using spherical harmonics.
• Utilized spherical harmonics to expand 1/|r-r'|, correlating to the Green function of the three-dimensional Laplacian.
• Determined the electric potential and subsequently calculated the electric field by taking the negative gradient.
• Successfully derived the electrostatic potential throughout space using the spherical harmonics approach.
• Calculated the electric field from the potential, demonstrating a more efficient method compared to direct integral evaluation.

Abstract