Electromagnetic field

The electromagnetic field is the central concept of the electromagnetism. It is defined starting from the components of the electromagnetic Force applying to a particle charged Q moving in a reference frame galiléen at the speed v . This force is expressed:

$\backslash \; vec\; \{F\}\; =\; Q\; (\backslash \; vec\; \{E\}\; +\; \backslash \; vec\; \{v\}\; \backslash \; and\; \backslash \; vec\; \{B\})$ where $\backslash \; vec\; \{E\}$ is the Electric field and $\backslash \; vec\; \{B\}$ is the Magnetic field. The electromagnetic field is the unit $(\backslash \; vec\; \{E\},\; \backslash \; \backslash \; vec\; \{B\})$.

The electromagnetic field is thus the composition of two Champ S vectorial S which one can measure independently. Nevertheless these two entities are indissociable:

• separation in magnetic and electric component is only one point of view depend on the reference frame of study,
• the Maxwell's equations governing the two components electric and magnetic are coupled, so that any variation of armature a variation of the other.

The behavior of the electromagnetic fields is described in a traditional way by more general way and the Maxwell's equations by the quantum electrodynamic .

The most general way to define the electromagnetic field is that of the electromagnetic Tenseur of the restricted Relativité.

Transformation galiléenne of the electromagnetic field

The value allotted to each component electric and magnetic of the electromagnetic field depends on the reference frame of study. Indeed one generally considers in static mode that the electric field is created by loads at rest while the magnetic field is created by loads moving (electric currents). Nevertheless the concept of rest and movement is relating to the reference frame of study.

Within the framework of relativity galiléenne, if one considers two reference frames of study galiléens (R) and (R'), with (R') and in uniform rectilinear motion speed V compared to (R), and if one calls v' the speed of a load Q in (R'), its speed in (R) is v = v' + V.

If one calls (E, B) and (E', B') the components of the electromagnetic field respectively in (R) and in (R'), the expression of the electromagnetic force having to be identical in the two reference frames one obtains the transformation of the electromagnetic fields thanks to:

$q\; E\; +\; (\backslash \; vec\; \{v\text{'}\}\; +\; \backslash \; vec\; V)\; \backslash \; and\; \backslash \; vec\; B\; =\; Q\; (\backslash \; vec\; \{E\text{'}\}\; +\; \backslash \; vec\; \{v\text{'}\}\; \backslash \; and\; \backslash \; vec\; \{B\text{'}\})$

This relation being true whatever the value of v' one a:

$\backslash \; vec\; \{B\text{'}\}\; =\; \backslash \; vec\; \{B\}$ and $\backslash \; vec\; \{E\text{'}\}\; =\; \backslash \; vec\; E\; +\; \backslash \; vec\; V\; \backslash \; and\; \backslash \; vec\; B$

See too

• electromagnetic Radiation

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