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The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form: [1] [2] = . Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.
The electromagnetic stress–energy tensor can be interpreted as the flux density of the momentum four-vector, and is a contravariant symmetric tensor that is the contribution of the electromagnetic fields to the overall stress–energy tensor: = (/ + / / / / / / /), where is the electric permittivity of vacuum, μ 0 is the magnetic ...
This is often described by saying that the electric field and magnetic field are two interrelated aspects of a single object, called the electromagnetic field. Indeed, the entire electromagnetic field can be represented in a single rank-2 tensor called the electromagnetic tensor; see below.
An electromagnetic field (also EM field) is a physical field, mathematical functions of position and time, representing the influences on and due to electric charges. [1] The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field .
The electromagnetic field is a covariant antisymmetric tensor of degree 2, which can be defined in terms of the electromagnetic potential by =.. To see that this equation is invariant, we transform the coordinates as described in the classical treatment of tensors: ¯ = ¯ ¯ ¯ ¯ = ¯ (¯) ¯ (¯) = ¯ ¯ + ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ = ¯ ¯ = ¯ ¯.
As the term suggests, an EM field consists of two vector fields, an electric field (,) and a magnetic field (,).Both are time-dependent vector fields that in vacuum depend on a third vector field (,) (the vector potential), as well as a scalar field (,)
In the relativistic formulation of electromagnetism, the nine components of the Maxwell stress tensor appear, negated, as components of the electromagnetic stress–energy tensor, which is the electromagnetic component of the total stress–energy tensor. The latter describes the density and flux of energy and momentum in spacetime.