Asymptotic potential of a rose-shaped disk

TL;DR

This paper analytically proves a conjecture about the asymptotic potential of a uniformly charged rose-shaped disk, which was previously supported only by numerical evidence, enhancing understanding of its electrostatic properties.

Contribution

It provides the first analytical proof confirming the asymptotic form of the potential of a rose-shaped disk, previously supported only by numerical evidence.

Findings

Analytical proof of the asymptotic potential form

Validation of previous numerical conjecture

Enhanced understanding of electrostatic potential behavior

Abstract

Based on extensive numerical evidence, a recent paper (Sheng Chen et al., Eur. J. Phys. {\bf 45} (2024), 045703) suggested that the potential of a uniformly charged rose-shaped disk in the plane of the disk has a simple asymptotic form. We present an analytical proof of this interesting conjecture.