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This gives the fields in a particular reference frame; if the reference frame is changed, the components of the electromagnetic tensor will transform covariantly, and the fields in the new frame will be given by the new components. In contravariant matrix form with metric signature (+,-,-,-),
If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
The E field and B field vary in space and time. Electromagnetic (EM) fields affect the motion of electrically charged matter: due to the Lorentz force. In this way, EM fields can be detected (with applications in particle physics, and natural occurrences such as in aurorae). In relativistic form, the Lorentz force uses the field strength tensor ...
The above transformation rules show that the electric field in one frame contributes to the magnetic field in another frame, and vice versa. [11] 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.
The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents, [note 4] matches the speed of light; indeed, light is one form of electromagnetic radiation (as are X-rays, radio waves, and others).
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 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: ¯ = ¯ ¯ ¯ ¯ = ¯ (¯) ¯ (¯) = ¯ ¯ + ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ = ¯ ¯ = ¯ ¯.
Gauss's law in its integral form is particularly useful when, by symmetry reasons, a closed surface (GS) can be found along which the electric field is uniform. The electric flux is then a simple product of the surface area and the strength of the electric field, and is proportional to the total charge enclosed by the surface.