Abstract
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.
Highlights
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
The objectives stem from the interest in the nonlinear oscillations of physical phenomena in conjunction with electrostatic related physics issues
We have overcome the challenges caused by this unevenness conducive calculating quantities such as electrostatic potential and electric field; these are seldomly discussed in scientific literature
Summary
It is viable to visualize a situation that by adjusting the relevant physical parameters such as the charges and the mass of the particle on one hand and the geometrical parameters such as the size of the ellipse as well as the initial position of the point charge and its initial velocity make the aforementioned forces compatible resulting oscillations. It is the goal of this investigation to quantifying the characteristics of the oscillations conducive to stable vibrations, identifying amplitude, period and related relevant characters. The values of the charges and the size of the ellipse chosen arbitrarily
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