Free rotation of conducting and dielectric spheres in a uniform electrostatic field

TL;DR

This paper analyzes the rotation dynamics of conducting and dielectric spheres in a uniform electrostatic field, deriving integrable equations and providing explicit solutions for various particle types.

Contribution

It introduces a detailed model of sphere rotation in electrostatic fields, including explicit solutions and analysis of dipole and torque dependencies.

Findings

Equations of rotary motion are integrable in quadratures.

Explicit solutions are provided for specific particle types.

Dipole moment and torque depend on angular velocity and electric properties.

Abstract

Rotation of conducting and dielectric spherical particles levitating in the uniform electrostatic field is considered. A dipole moment of the spherical particle induced by the external uniform electrostatic field is inclined to the field if the particle rotates. This causes the torque braking the rotation. Vectors of dipole moment and torque depend both on an angular velocity of the particle and its electric properties. Equations of rotary motion of the particle levitating in the external field are integrable in quadratures. Few examples of the conducting and dielectric particles are solved explicitly.