Forces on Fields

TL;DR

This paper explores the analogy between electromagnetic fields and relativistic fluids, analyzing how forces act on the field itself and clarifying the field's inertial properties and stress tensor in electromagnetism.

Contribution

It introduces a novel perspective by emphasizing forces acting on the electromagnetic field, enhancing understanding of the field's inertial role and the interpretation of Maxwell's stress tensor.

Findings

Electromagnetic fields behave like relativistic fluids.

Forces on the field are analogous to fluid forces.

Insights into the inertial properties of electromagnetic fields.

Abstract

In electromagnetism, as in Newton's mechanics, action is always equal to reaction. The force from the electromagnetic field on matter is balanced by an equal and opposite force from matter on the field. We generally speak only of forces exerted by the field, not forces exerted upon the field. But, we should not be hesitant to speak of forces acting on the field. The electromagnetic field closely resembles a relativistic fluid and responds to forces in the same way. Analyzing this analogy sheds light on the inertial role played by the field's mass, the status of Maxwell's stress tensor, and the nature of the electromagnetic field.