An exact one-dimensional integral formula gives the electrostatic potential of a disk whose charge density is (1-u^2)^nu u^p, and numerical plots reveal a crossover in the in-plane potential shape around p=-0.34.
Eyges,The Classical Electrodynamic Field(Dover, New York, 2012)
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Modeling the Electrostatic Potential of Disks with Arbitrary Radial Charge Profiles
An exact one-dimensional integral formula gives the electrostatic potential of a disk whose charge density is (1-u^2)^nu u^p, and numerical plots reveal a crossover in the in-plane potential shape around p=-0.34.