What Are Retarded Time and Position in Electrodynamics?

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SUMMARY

The discussion clarifies the concepts of retarded time and retarded position in electrodynamics. Retarded time is defined by the equation t = t_r + r/c, where t represents the present time, t_r is the time elapsed since the electromagnetic information reached the observation point, and r/c is the time taken for that information to travel. The retarded position, denoted as w(t_r), indicates the position of a particle at the time when the electromagnetic signal first reached it, contrasting with w(t), which represents its current position.

PREREQUISITES
  • Understanding of basic electrodynamics principles
  • Familiarity with the concept of electromagnetic waves
  • Knowledge of the speed of light (c) in a vacuum
  • Basic mathematical skills for manipulating equations
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  • Study the implications of retarded time in electromagnetic theory
  • Explore the relationship between retarded position and wave propagation
  • Learn about the applications of retarded time in advanced electrodynamics
  • Investigate the role of retarded time in the context of special relativity
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Students and professionals in physics, particularly those focusing on electrodynamics, as well as educators seeking to clarify these concepts for their students.

AriAstronomer
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Hey everyone,
Just a quick question about a few electrodynamic concepts:

1) retarded time: t = t_r - (curly)r/c. Is t = total time, t_r = time elspased since the electromagnetic 'news' reached the point in question, and r/c = time taken to reach the point in question?

2) I'm a bit confused about w(t_r), the retarded position. Is this the position of a particle when some electromagnetic 'news' first reached it, and is now currently at a different position? How does it differ from w(t)?

Thanks.
Ari
 
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Your 1st equation should be:

t=t_r+r/c

where t is the present time, t_r was the time r/c ago from the present time.

w(t_r) stands for the position of a particle at a time r/c before the present time.
 

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