Abstract
Two electrically charged rings of different sizes are assembled along their common vertical symmetry axis through their centers. The bottom ring is secured on a horizontal support while the top one is loose. For a set of practical values characterizing the charged rings we envision a scenario where the mutual electric repulsion between the rings and the weight of the top ring results in stable nonlinear oscillations. To quantify the characteristics of the oscillations, we utilize a Computer Algebra System specifically Mathematica [1]. We accompany the analysis with a simulation for a comprehensive visual understanding.
Highlights
Two electrically charged rings of different sizes are assembled along their common vertical symmetry axis through their centers
The same comment is true for popular mathematical physics texts e.g. [5]
In this investigating research article as a sample example we show how we have extended a topic that is hardly discussed in both references [2] [3] and how we have intertwined the analysis in the spirt of a mathematical physics issue [5] with a Computer Algebra System (CAS), Mathematica [1]
Summary
Charging both rings positively (negatively) creates repulsive electrostatic force. The floating ring being massive gets pull down by its weight. To quantify the oscillations conducive to the relevant quantities such as: frequency, period, and amplitude, one needs to establish the equation of motion. The latter requires a methodology, meaning either the mutual interactive force between the rings are to be considered or from energy point of view of their electrostatic potential energy. The former requires calculation of the electric field of the bottom ring at off axis region where the floating ring is at, where the latter calls for evaluation of associated electrostatic potential.
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