The inequality between size and charge in spherical symmetry

TL;DR

This paper proves a sharp inequality relating the size and charge of spherically symmetric bodies, showing that twice the radius exceeds the charge, with implications for understanding physical constraints.

Contribution

The paper establishes a new sharp inequality between size and charge in spherical symmetry, including proofs, physical implications, and numerical illustrations.

Findings

Twice the radius is always greater than the charge for spherically symmetric bodies.

The inequality proven is sharp, meaning it cannot be improved.

Numerical examples support the theoretical results.

Abstract

We prove that for a spherically symmetric charged body two times the radius is always strictly greater than the charge of the body. We also prove that this inequality is sharp. Finally, we discuss the physical implications of this geometrical inequality and present numerical examples that illustrate this theorem.