Retarded time

 ( Time ) 

In electromagnetism, an electromagnetic wave (light) in vacuum travels at a finite speed (the speed of light c). The retarded time is the propagation delay 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" calculation for EM (Electro-Magnetic) 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. 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′.Electromagnetism (2nd Edition), I.S. Grant, W.R. Phillips, Manchester Physics, John Wiley & Sons, 2008, Introduction to Electrodynamics (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007,

The retarded time is: $t\text{'}\; =\; t\; -\; \backslash frac$

{c}

(which can be rearranged to $c\; =\; |\backslash mathbf\{r\}-\backslash mathbf\{r\}\text{'}|\; /\; (t\; -\; t\text{'})$, 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 “−”:

$t\_a\; =\; t\; +\; \backslash frac${ c}

This is the time it takes for a field to propagate from originating at the present time t to a distance $|\backslash mathbf\{r\}-\backslash mathbf\{r\}\text{'}|$. Corresponding to retarded and advanced times are retarded and advanced potentials.McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994,

---

Retarded position The retarded position r' (the position where an EM wave emitted at the retarded time t') 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:

$\backslash mathbf\{r\}-\backslash mathbf\{r\text{'}\}\; =\; \backslash mathbf\{r\}-\backslash left(\; \backslash mathbf\{r\_c\}-\backslash frac${c}\mathbf{v} \right) = \mathbf{r}-\mathbf{r_c}+\frac{c}\mathbf{v},

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 ρ( r , t_r) and current density J (r, t_r) 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.

---

See also

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

Post Comment