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

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.