On the geometric dynamics of the charged point-particle propagated through the spherical optical fiber

Abstract

In this manuscript, we basically focus on the geometric dynamics of the charged particle propagation through the spherical frame. To be able to investigate this process, we suppose that the trajectory of the linearly polarizable light coincides with the path of the point-particle having charges, in which this action is exerted to take place along with the optical fiber designated by the spherical frame on the unit two-sphere. We prove in an elegant fashion that two famous parallel transportations i.e. Fermi-Walker parallel transportation and Rytov parallel transportation are applicable for our case so that we can obtain the geometric phase of the charged point-particle. Later, we present a description of spherical electromagnetic curves on the unit sphere by using the fundamental definition of the Lorentz force and electromagnetic force of the charged point-particle. We further apply our findings to compute the optical magnetic-torque, optical linear and angular momentum, energy-exchanges rate, Poynting vector, electromagnetic force, etc. to comprehend the physical dynamics of the moving charged particle.