Maxwell stress tensor

With electromagnetic momentum density

g = ϵ_{0} E \times B

, the momentum-flux convention

σ_{ij} = - ϵ_{0} E_{i} E_{j} + \frac{ϵ _{0}}{2} E^{2} δ_{ij} - \frac{1}{μ _{0}} B_{i} B_{j} + \frac{1}{2 μ _{0}} B^{2} δ_{ij}

satisfies

\partial_{t} g_{j} + \partial_{i} σ_{ij} = - (ρ E + J \times B)_{j} .

Table of contents

Electromagnetic momentum density ( $g = ϵ_{0} E \times B = S / c^{2}$ )

The electromagnetic momentum density in vacuum is

g = ϵ_{0} E \times B

. It equals the Poynting vector divided by

c^{2}

, expressing the relativistic relation between energy flux and momentum density.

Local conservation of electromagnetic momentum

With the momentum-flux sign convention used for the Maxwell stress tensor, Maxwell's equations imply

\nabla \cdot σ + \partial_{t} g = - f_{L},

where

g

is the electromagnetic momentum density and

f_{L}

is the Lorentz force density exerted by the field on matter. Thus total field-plus-matter momentum is locally conserved.

Radiation pressure on a perfectly absorbing surface

A normally incident vacuum wave of time-averaged intensity

I

transfers momentum

I / c

per unit area and time to a perfectly absorbing surface, so its radiation pressure is

p = \frac{I}{c} .

A perfect reflector reverses the normal momentum and gives

2 I / c

.

 Ancestors (4)

 Incoming links (20)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Maxwell stress tensor by

Wikipedia Bot  1

The Maxwell stress tensor is a mathematical construct used in electromagnetism to describe the distribution of electromagnetic forces in a continuous medium. It encapsulates the effects of electric and magnetic fields on the momentum and stress within a material that is subjected to electromagnetic fields.

 Read the full article

  See all articles in the same topic Create my own version