Undergrad What are the Relativistic versions of Jefimenko's equations?

[tade]

I would like to know what the Special Relativistic versions of Jefimenko's equations are.An example of a noticeable difference between non-relativistic and relativistic cases is considering Jefimenko's equation for the B-field, for a magnetostatic circular current loop.

Jefimenko's B-field equation yields the magnitude of the B-field at the center of the loop similar to that of the Biot-Savart Law. (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c2)

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With the effects of special relativity in consideration, the magnitude of the B-field at the center of the loop is the Jefimenko/Biot-Savart magnitude multiplied by the Lorentz factor.

The Lorentz factor is based on the speed(s) of the moving electric charges whizzing about the circular loop.

So if you increase the speed of the charges, while keeping the magnitude of the current constant, the magnitude of the B-field will increase.

 

[PeterDonis]

I would like to know what the Special Relativistic versions of Jefimenko's equations are.

AFAIK they already are, assuming you're referring to the equations in terms of retarded potentials. But we need a reference to be sure; see below.

Jefimenko's B-field equation

Please give a reference for where you are getting Jefimenko's equations from.

 

[Dale]

We will leave this closed until a reference is provided.