Impact of a Bumpy Nonuniform Electric Field on Oscillations of a Massive Point-Like Charged Particle

Abstract

As a general feature, the electric field of a localized electric charge distribution diminishes as the distance from the distribution increases; there are exceptions to this feature. For instance, the electric field of a charged ring (being a localized charge distribution) along its symmetry axis perpendicular to the ring through its center rather than as expected being a diminishing field encounters a local maximum &#8220;bump&#8221;. It is the objective of this research-oriented study to analyze the impact of this bump on the characteristics of a massive point-like charged particle oscillating along the symmetry axis. Two scenarios with and without gravity along the symmetry axis are considered. In addition to standard kinematic diagrams, various phase diagrams conducive to a better understanding are constructed. Applying Computer Algebra System (CAS), <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> most calculations are carried out symbolically. Finally, by assigning a set of reasonable numeric parameters to the symbolic quantities various 3D animations are crafted. All the CAS codes are included.