# Retarded time

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In electromagnetism, electromagnetic waves in vacuum travel at the speed of light *c*, according to Maxwell's Equations. The **retarded time** is the time when the field began to propagate from a point in a charge distribution to an observer. The term "retarded" is used in this context (and the literature) in the sense of propagation delays.

## Retarded and advanced times

The calculation of the retarded time *t _{r}* is nothing more than a simple "speed-distance-time" calculation for EM fields.

If the EM field is radiated at position vector **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*, so subtracting this delay from the observer's time *t* gives the time when the field *actually began to propagate* - the retarded time^{[1]}^{[2]}

which can be rearranged to

showing how the positions and times correspond to source and observer.

Another related concept is the **advanced time** *t _{a}*, which takes the same mathematical form as above:

and is so-called since this is the time the field will advance from the present time *t*. Corresponding to retarded and advanced times are retarded and advanced potentials.^{[3]}

## Application

Perhaps surprisingly - electromagnetic fields and forces acting on charges depend on their history, not their mutual separation^{[4]}. The calculation of the electromagnetic fields at a present time includes integrals of charge density ρ(**r'**, *t _{r}*) and current density

**J**(

**r'**,

*t*) using the retarded times and source positions. The quantity is prominent in electrodynamics, electromagnetic radiation theory, and in Wheeler-Feynman absorber theory, since the history of the charge distribution affects the fields at later times.

_{r}## See also

- Antenna measurement
- Electromagnetic four-potential
- Jefimenko's equations
- Liénard–Wiechert potential
- Light-time correction

## References

- ↑ Electromagnetism (2nd Edition), I.S. Grant, W.R. Phillips, Manchester Physics, John Wiley & Sons, 2008, ISBN 9-780471-927129
- ↑ Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ISBN 81-7758-293-3
- ↑ McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3
- ↑ Classical Mechanics, T.W.B. Kibble, European Physics Series, McGraw-Hill (UK), 1973, ISBN 07-084018-0