Retarded Potentials

retarded potentials

[ri′tärd·əd pə′ten·chəlz]
(electromagnetism)
The electromagnetic potentials at an instant in time t and a point in space r as a function of the charges and currents that existed at earlier times at points on the past light cone of the event r,t.

Retarded Potentials

 

the potentials of a variable electromagnetic field that take into account the retardation of changes in the field at each point of space with respect to the change in the charges and currents that create the field and are located at other points in space. The potentials of the electromagnetic field characterize this field along with the strengths of the electric and magnetic fields (E and H). If at some moment of time t there takes place a change in the distribution of charges or currents, then at some distance from them, because of the finite velocity (c) of propagation of the electromagnetic field, this change will be manifested not immediately, not at the same moment t, but after some delay. Therefore the value of the potentials at time t at a given point in space located at a distance R from the field source is determined by the charge and current densities that existed at the previous moment of time τ = tR/c. Here R/c is the delay time, that is, the time needed for the disturbance of the electromagnetic field to reach the point at which the field is measured. Potentials of this type are called retarded potentials. If the charges and currents are continuously distributed in space, then the potentials are determined by integrating the elementary retarded potentials created by the charges and currents in certain very small volumes of space.

REFERENCE

Tamm, I. E. Osnovy teorii elektrichestva, 7th ed. Moscow-Leningrad, 1957. Chapter 7.

G. IA. MIAKISHEV

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To this end, we had to introduce retarded potentials consisting of scalar and vector potentials to treat the radiation from a MTL system.
These retarded potentials satisfy the above differential equations for the scalar and vector potentials [39, 40].
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The retarded potentials have both the real and imaginary parts, when expressed for AC with a fixed frequency.
Chapter 5 derives the retarded potentials for a general distribution of charge and current.