- Electromagnetic stress-energy tensor
physics, the electromagnetic stress-energy tensor is the portion of the stress-energy tensordue to the electromagnetic field.
In free space in
SI units, the electromagnetic stress-energy tensor is:And in explicit matrix form::,
Poynting vector,: electromagnetic field tensor,: Minkowski metrictensor , and: Maxwell stress tensor.Note that where "c" is light speed.
In free space in
cgs units, we simply substitute with and with ::And in explicit matrix form::
Poynting vectorbecomes the form: :.
The stress-energy tensor for an electromagnetic field in a
dielectricmedium is less well understood and is the subject of the unresolved Abraham-Minkowski controversy(however see Pfeifer et. al, Rev. Mod. Phys. 79, 1197 (2007)).
The element, , of the energy momentum tensor represents the flux of the μth-component of the
four-momentumof the electromagnetic field, , going through a hyperplane. It represents the contribution of electromagnetism to the source of the gravitational field (curvature of space-time) in general relativity.
The electromagnetic stress-energy tensor allows a compact way of writing the conservation laws of linear momentum and energy by electromagnetism.:
where is the density of the (3D) Lorentz force on matter.
This equation is equivalent to the following 3D conservation laws::
where:Electromagnetic energy density (joules/meter3) is :
Poynting vector(watts/meter2) is :Density of electric current(amperes/meter2) is :Electromagnetic momentum density (newton·seconds/meter3) is : Maxwell stress tensor(newtons/meter2) is :Density of electric charge(coulombs) is
Covariant formulation of classical electromagnetism
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