On the investigation of two non-neutral static bodies

TL;DR

This paper explores the static equilibrium of two non-neutral bodies, introduces a function resembling nuclear models, and uncovers a new quantity called quintessence related to electric potential and Legendre polynomials.

Contribution

It introduces a novel function Y(A,θ) related to non-neutral bodies and defines the concept of quintessence, linking it to electric potential and Legendre polynomials.

Findings

No solution for zero net field under given boundary conditions.

The function Y(A,θ) resembles nuclear empirical functions.

Quintessence behaves like electric potential and generates Legendre polynomials.

Abstract

In this work, we have considered statics of two non-neutral bodies unaffected by external force fields. We have tried to calculate the value of $\theta$ at which net field strength becomes zero however under given boundary condition, we get no solution. Thereafter, We define a function $Y(A,\theta)$, it can be found that the function $Y$ mathematically resembles to Semi-mass empirical function $M(Z,A)$ that exists in nuclear model. Further investigations on $Y$ has shown that \textit{the nature gives double preference to a system , which is having heavier object at center of positive charge over another negative charged body}. Meanwhile, we come across another expression which depicts about the geometry of ellipse in complex plane under certain conditions, Whose physical significance is yet to be get realized. Lastly, we have investigated a case associated with non-zero net field. As a result of it, we define a new quantity as \textit{quintessence}, which behaves analogous to the electric potential, and it is mathematically turned out to be a generating function for Legendre polynomials, which also highlights the previous statement about nature's selective behaviour. We have tried to verify the constancy of a factor $\chi$ which runs throughout the various expressions in this study of statics, it is indeed found to be almost constant but highly sensitive to scale or order of size of the subject under study.