On the Electromagnetic Mass Dilemma

TL;DR

This paper resolves the electromagnetic mass dilemma by deriving a velocity-dependent electromagnetic mass expression for a charged sphere, reconciling classical and relativistic calculations of electromagnetic mass.

Contribution

It introduces a velocity-dependent formula for electromagnetic mass that unifies classical and relativistic results for a charged sphere.

Findings

Electromagnetic mass depends on velocity as 4/(3+(v/c)^2) times E/c^2.

The derived formula reconciles classical and relativistic electromagnetic mass calculations.

Provides a consistent expression for electromagnetic mass at any velocity.

Abstract

We show that a charged sphere moving at a constant velocity $v$ exhibits a mass due to electromagnetic radiation, expressed as $4/(3+(v/c)^2) (E/c^2)$, where $E$ is the electromagnetic energy and $c$ the speed of light in vacuum. Our finding reconciles the longstanding mismatch between the electromagnetic mass calculated from the classical electrodynamics' $4/3 (E/c^2)$ and the relativistic theory.