Impact of Eccentricity on Nonlinear Oscillations of a Point-Like Charge in the Electric Field of a Curvature-Dependent Elliptic Charged Ellipse

Calculation of the interactive force between two horizontally stacked circular uniformly charged rings placed along the common vertical axis conducive to nonlinear oscillations under gravity has been addressed [1]. Although challenging, nonetheless the scope of the study limited to uniform charge distributions of the rings. Here we extend the analysis considering a charged ellipse with a nonuniform, curvature-dependent elliptic charge distribution exerting a force on a point-like charge placed on the vertical symmetry axis. Nonuniform charge distribution and its impact on various practical scenarios are not a common theme addressed in literature. Applying Computer Algebra System (CAS) particularly Mathematica [2], we analyze the issue on hand augmenting the traditional scope of interest. We overcome the CPU expensive symbolic computation following our newly developed numeric/symbolic method [1]. For comprehensive understanding, we simulate the nonlinear oscillations.