Maxwell Tensor

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  -E1 -E2 -E3)
(E1  0   B3 -B2)
(E2 -B3  0   B1)
(E3  B2 -B1  0 )

an is an antisymmetric tensor (ie. reversing the indices changes the sign). Note that F_i0=-F₀₁=E_i and F_ij=ε_ijkB_k. In physcial law, it manifests itself in the relativistc form of the Lorentz Equation:

F^μ=qF^μ_νv^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_μF^μν=-μ₀j^ν