Energy, Forces, Fields and the Lorentz Force Formula

TL;DR

This paper presents a unified approach to defining energy, momentum, and forces for particles in fields, deriving the Lorentz force law and generalizing Newton's second law.

Contribution

It introduces a simple energy decomposition method to derive general force definitions and extends Newton's law to encompass electromagnetic forces.

Findings

Derives the Lorentz force law from energy considerations

Provides a generalized Newton's second law for particles in fields

Connects energy decomposition with Lagrangian mechanics

Abstract

We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted on the particle by fields, followed by the generalization of Newton's second law to accomodate these generally defined forces. We show that our generalization implies the Lorentz force law as well as Lagrange's equation, along with the usually accepted Lagrangian and the associated velocity dependent potential of a moving charged particle.