User:Maschen/Momentum density

In physics, momentum density of a continuum or field is simply the momentum per unit volume of the continuum or field. The SI units are kg s−1 m−2, or dimensions are [M][T][L]−2. There is no standard symbol, this article will use π. There are a number of occurrences throughout physics.

Field
For a field

Continuum
For a continuum with density ρ at a point x inside the current configuration of the continuum, we have


 * $$\boldsymbol{\pi} = \rho \mathbf{v}$$

Integrating over the region the continuum occupies gives the total momentum of the continuum


 * $$\mathbf{p} = \int_R dV \boldsymbol{\pi} $$

with dV the differential volume element.

Occurances
The stress-energy tensor electromagnetic field has momentum. The momentum density is

The electromagnetic field has momentum. The momentum density is