The electromagnetic field outside the steadily rotating relativistic uniform system

TL;DR

This paper derives approximate formulas for the electromagnetic field outside a uniformly rotating relativistic charged sphere, analyzing how rotation affects potentials and fields at various zones and comparing with Laplace equations.

Contribution

It provides new approximate expressions for electromagnetic potentials and fields outside a rotating relativistic sphere, assessing their dependence on angular velocity and geometry.

Findings

Potentials and fields increase near the sphere's surface and equator with rotation.

Additions to potentials are proportional to the square of angular velocity and radius.

Maximum increase in fields could reach 4% for a charged neutron star and 54% for a proton.

Abstract

Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and far zones the corresponding expressions are found for the scalar and vector potentials, as well as for the electric and magnetic fields. Then these expressions are assessed for correspondence to the Laplace equations for potentials and fields. One of the purposes is to test the truth of the assumption that the scalar potential and the electric field depend neither on the value of the angular velocity of rotation of the sphere nor on the direction to the point where the field is measured. However, calculations show that potentials and fields increase as the observation point gets closer to the sphere's equator and to the sphere's surface, compared with the case for a stationary sphere. In this case, additions are proportional to the square of the angular velocity of rotation, the square of the sphere's radius and inversely proportional to the square of the speed of light. The largest found relative increase in potentials and fields could reach the value of 4% for the rapidly rotating neutron star PSR J1614-2230, if the star were charged. For a proton, a similar increase in fields on its surface near the equator reaches 54%.