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
Fμν (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=-F
01=E
i and F
ij=
εijkB
k. In physcial law, it manifests itself in the
relativistc form of the
Lorentz Equation:
Fμ=qFμνvν
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;
dμFμν=-μ0jν