General Relativity: An Introduction for Physicists · Problem 6.3

Electromagnetism — Hobson, Efstathiou & Lasenby

Physics · electromagnetic-field-strength-tensor

Problem

In some Cartesian inertial frame

S

, the contravariant components of the electric and magnetic fields are

E^i

and

B^i

respectively. Show that the corresponding electromagnetic field-strength tensor has the contravariant components

[F^{\mu\nu}] = \begin{pmatrix} 0 & -E^1/c & -E^2/c & -E^3/c \\ E^1/c & 0 & -B^3 & B^2 \\ E^2/c & B^3 & 0 & -B^1 \\ E^3/c & -B^2 & B^1 & 0 \end{pmatrix}.