A

tensorial quantity used in

Relativistic Electrodynamics which incorporates both the

electric field and the

magnetic field. Not invented by

James Clerk Maxwell, but named after him, just to be kind (also called the field strength tensor).

It is written as

F_{μν} (you may want to read about the

abstract index notation at this point), and has components:

(0 -E_{1} -E_{2} -E_{3})
(E_{1} 0 B_{3} -B_{2})
(E_{2} -B_{3} 0 B_{1})
(E_{3} B_{2} -B_{1} 0 )

an is an antisymmetric tensor (ie. reversing the indices changes the sign). Note that F

_{i0}=-F

_{01}=E

_{i} and F

_{ij}=

ε_{ijk}B

_{k}. In physcial law, it manifests itself in the

relativistc form of the

Lorentz Equation:

F^{μ}=qF^{μ}_{ν}v^{ν}

giving the electromagnetic 4-force on a patricle with charge q and 4-velocity v

^{ν}. It is generated by the 4-current j

^{ν}=(ρ,

**j**)

^{T};

d_{μ}F^{μν}=-μ_{0}j^{ν}