In electromagnetism, the electromagnetic tensor, or electromagnetic field tensor, F, is defined as: Electromagnetism is the physics of electromagnetic fields: a field, encompassing all of space, comprised of electrical and magnetic fields. ...

where Aⁱ is the vector potential. In vector calculus, a vector potential is a vector field which generates a solenoidal vector field. ...

Then A_i is the covariant form of a tensor (or vector) which has components In category theory, see covariant functor. ... In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalar, vector and linear operator. ...

(φ/c, -A_x, -A_y, -A_z);

while Aⁱ, the contravariant form, has components Contravariant is a mathematical term with a precise definition in tensor analysis. ...

(φ/c, A_x, A_y, A_z).

Properties

The Electromagnetic Field Tensor is:

• antisymmetric, F^ik = − F^ki

In set theory, the adjective antisymmetric usually refers to an antisymmetric relation. ...

Value

In terms of the electric field, E, the magnetic field, B, and the speed of light, c; the electromagnetic field tensor is: In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Current flowing through a wire produces a magnetic field (M) around the wire. ... Cherenkov effect in a swimming pool nuclear reactor. ...