Interaction potential between coplanar uniformly charged disk and ring

Abstract

We consider a system made up of a uniformly charged disk and a uniformly charged ring that are coplanar with each other. The disk and ring have arbitrary radii and contain arbitrary amounts of net charge that is spread uniformly over area and length, respectively. This study is seen as the first necessary step towards a classical model treatment of a two-dimensional system of electrons in a weak perpendicular magnetic field. In this scenario, the uniformly charged disk represents the neutralizing background in a jellium approximation while a uniformly charged ring is viewed as a classical approximation to the cyclotron motion of the electron in presence of a uniform perpendicular magnetic field. In this work, we obtain an exact integral expression for the interaction potential energy of the system as a function of the separation distance between the centers of the two bodies and discuss various emerging features of this model.

Keywords

• Potential energy
• Uniformly charged disk
• Uniformly charged ring
• Integer quantum Hall effect
• Fractional quantum Hall effect