The potential of a uniformly charged planar structure with shape of a rose curve

Abstract

The electric potential U(θ) of a uniformly charged plane with a rose-curve shape (referred to as a "rose disk") satisfies a 'roselike curve function,' and there exists an asymptotic expression for the potential when the observation point is far from the rose disk. To validate the accuracy of the model, a constant electric current field was employed to simulate the electrostatic field. The potential distribution characteristics of uniformly charged circular discs and trilobal rose discs in the experimental setting were equivalently obtained by the experiment of electrolytic tank. The results indicate that under the non-idealized constraints of real experimental conditions, the asymptotic formula can be used as an analytical method to quickly study the rose disk potential.