A uniformly charged circular disk with an anisotropic Coulomb interaction potential

We consider a uniformly charged circular disk containing elementary charges that interact with an anisotmpic Coulomb interaction potential. Such an anisotmpic Coulomb interaction potential has been recently considered within the framework of a two-dimensional system of electrons in the quantum Hall regime. The anisotropy of the potential is introduced by a phenomenological parameter that can be tuned continuously as to incorporate the standard isotropic Coulomb interaction potential as a special case. The energy of the uniformly charged circular disk is calculated exactly for the given anisotropic interaction potential as a function of the anisotropy parameter. The results obtained are related to electrostatic problems that involve uniformly charged flat elliptical plates and may be useful to understand finite two-dimensional systems of electrons in the quantum Hall regime in which all point charges interact with the anisotropic Coulomb interaction potential presently considered.