# Electromagnetic Field Momentum

## Electromagnetic Field Momentum

a dynamic characteristic of a field—the momentum that the electromagnetic field possesses in a given volume. Bodies placed in an electromagnetic field are acted upon by mechanical forces. In this case the action of the field upon the body is associated with the absorption of electromagnetic waves by the body or with a change in the propagation direction of the waves (reflection, scattering, refraction). If the body radiates electromagnetic waves, specifically light waves, the momentum of the body is also changed. Since the momentum of a closed material system cannot be changed by radiation, absorption, or reflection of electromagnetic waves (according to the law of conservation of total momentum of a system), it follows that an electromagnetic wave also has a momentum. The existence of electromagnetic field momentum was first demonstrated by experiments with light pressure (P. N. Lebedev, 1899).

The classical electromagnetic field theory (Maxwell equations) shows that the electromagnetic field momentum is distributed in a space with a volume density, g = (1/4TTC) [EH]— in the cgs (Gauss) system—or g = (1/c2) [EH]—in the International System of Units—where [EH] is the vector product of the intensities of electric field E and magnetic field H numerically equal to EH sinα (α is the angle between E and H) and c = 3 X 1010 cm/sec, the velocity of light in a vacuum. Thus the electromagnetic field momentum density vector g is perpendicular to E and H and is directed along the forward motion of a right-hand screw rotating from E to H.

In the quantum electromagnetic field theory (quantum electrodynamics) carriers of field energy and field momentum are quanta of this field—photons. A photon of a frequency v has an energy hv and a momentum hv/c, where h is Planck’s constant. The existence of photon momentum is demonstrated by many phenomena. For instance, a momentum transfer between an electromagnetic field and a particle takes place in Compton’s effect (the elastic scattering of photons by electrons).

G. V. VOSKRESENSKII [(10–484–1]

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