electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, an

electromagnetic wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...

(light) in

vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

travels at a finite speed (the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

''c''). The retarded time is the

propagation delay Propagation delay is the time duration taken for a signal to reach its destination, for example in the electromagnetic field, a wire, speed of sound, gas, fluid or seismic wave, solid body. Physics * An electromagnetic wave travelling through ...

between emission and observation, since it takes time for information to travel between emitter and observer. This arises due to causality.

Retarded and advanced times

Retarded time ''t_r'' or ''t''′ is calculated with a " speed-distance-time" calculation for EM fields. If the EM field is radiated at

position vector In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point ''P'' in space. Its length represents the distance in relation to an arbitrary reference origin ''O'', and ...

r′ (within the source charge distribution), and an observer at position r measures the EM field at time ''t'', the time delay for the field to travel from the charge distribution to the observer is , r − r′, /''c''. Subtracting this delay from the observer's time ''t'' then gives the time when the field began to propagate, i.e. the retarded time ''t''′. The retarded time is:

t' = t - \frac

(which can be rearranged to

c = , \mathbf-\mathbf',  / (t - t')

, showing how the positions and times of source and observer are causally linked). A related concept is the advanced time ''t_a'', which takes the same mathematical form as above, but with a “+” instead of a “−”: :

t_a = t + \frac

This is the time it takes for a field to propagate from originating at the present time ''t'' to a distance

, \mathbf-\mathbf',

. Corresponding to retarded and advanced times are retarded and advanced potentials.

Retarded position

The retarded position can be obtained from the current position of a particle by subtracting the distance it has travelled in the lapse from the retarded time to the current time. For an inertial particle, this position can be obtained by solving this equation: :

\mathbf-\mathbf = \mathbf-\mathbf+\frac\mathbf

, where r_c'' is the current position of the source charge distribution and v its velocity.

Application

Perhaps surprisingly - electromagnetic fields and forces acting on charges depend on their history, not their mutual separation.Classical Mechanics, T.W.B. Kibble, European Physics Series, McGraw-Hill (UK), 1973, The calculation of the electromagnetic fields at a present time includes integrals of

charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...

ρ(r', ''t_r'') and

current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ...

J(r', ''t_r'') using the retarded times and source positions. The quantity is prominent in

electrodynamics In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...

theory, and in

Wheeler–Feynman absorber theory The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is a theory of electrodynamics based on a relativistic correct ...

, since the history of the charge distribution affects the fields at later times.

References

{{DEFAULTSORT:Retarded Time Time Electromagnetic radiation

Retarded and advanced times

Retarded position

Application

See also

References