Retarded and Advanced Times
The calculation of the retarded time tr 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
which can be rearranged to
showing how the positions and times correspond to source and observer.
Another related concept is the advanced time ta, 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.
Read more about this topic: Retarded Time
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