# Electromagnetic Field

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## Electromagnetic field

A changing magnetic field always produces an electric field, and conversely, a changing electric field always produces a magnetic field. This interaction of electric and magnetic forces gives rise to a condition in space known as an electromagnetic field. The characteristics of an electromagnetic field are expressed mathematically by Maxwell's equation. See Electric field, Electromagnetic radiation, Electromagnetic wave

## Electromagnetic Field

a special form of matter that mediates the interaction between charged particles (seeFIELD).

In a vacuum, an electromagnetic field is characterized by the electric field strength E and the magnetic flux density B, which determine the forces exerted by the field on stationary or moving charged particles. In addition to the vectors E and B, which are measured directly, an electromagnetic field may be characterized by a scalar potential φ and a vector potential A. The potentials are not uniquely determined, a gauge transformation being required.

In a medium, an electromagnetic field is also characterized by the following two auxiliary vector quantities: the magnetic field strength H and the electric flux density D (seeINDUCTION, ELECTRICAL AND MAGNETIC).

The behavior of electromagnetic fields is a subject of classical electrodynamics. In an arbitrary medium, the behavior of such fields is described by Maxwell’s equations. The equations make it possible to determine the fields as a function of the distributions of charge and current.

Microscopic electromagnetic fields, which are produced by individual elementary particles, are characterized by the strengths of the microscopic electric field (e) and the microscopic magnetic field (h). The mean values of the microscopic field strengths are related to the macroscopic characteristics of an electromagnetic field in the following way: ē = E and h̄ = B. Microscopic fields satisfy the Lorentz-Maxwell equations.

The electromagnetic field of stationary charged particles or of charged particles moving with constant velocity is inseparably bound to the particles. When particles are accelerated, their electromagnetic field is “torn away” and exists independently in the form of electromagnetic waves.

The generation of an electromagnetic field by an alternating magnetic field and the generation of a magnetic field by an AC electric field show that alternating electric and magnetic fields do not exist separately, that is, are not independent of one another. According to the theory of relativity, the components of the vectors that characterize an electromagnetic field form a single physical quantity called the electromagnetic field tensor. The components of the tensor are transformed upon a transition from one inertial reference frame to another, in accordance with the Lorentz transformations.

At high field frequencies, the quantum properties of an electromagnetic field become important. In this case, classical electrodynamics is not applicable and an electromagnetic field is described by quantum electrodynamics.

### REFERENCES

Tamm, I. E. Osnovy teorii elektrichestva, 9th ed. Moscow, 1976.
Kalashnikov, S. G. Elektrichestvo, 4th ed. Moscow, 1977. (Obshchii kurs fiziki, vol. 2.)
Feynman, R., R. Leighton, and M. Sands. Feinmanovskie leklsii po fizike, vols. 5–7. Moscow, 1966–67.
Landau, L. D., and E. M. Lifshits. Teoriia polia, 6th ed. Moscow, 1973. (Teoreticheskaia fizika, vol. 2.)
Landau, L. D., and E. M. Lifshits. Elektrodinamika sploshnykh sred. Moscow, 1959.

G. IA. MIAKISHEV

## electromagnetic field

[i¦lek·trō·mag′ned·ik ′fēld]
(electromagnetism)
An electric or magnetic field, or a combination of the two, as in an electromagnetic wave.
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