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This page shows solutions for Maxwell's equations of the electric and magnetic potentials (Eqn.s (509) and (510)):

http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

They are derived with the aid of a Green's function: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html

They make use of retarded time.

I'm looking for a solution in terms of instantaneous time. If I swap the retarded time variables in 509 & 510 with instantaneous time, would those be mathematically valid solutions?

And if not, what should I modify?

Also, if my intuition is correct, although the retarded time involves the speed of light, any arbitrary speed will be a valid solution right?

http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

They are derived with the aid of a Green's function: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html

They make use of retarded time.

I'm looking for a solution in terms of instantaneous time. If I swap the retarded time variables in 509 & 510 with instantaneous time, would those be mathematically valid solutions?

And if not, what should I modify?

Also, if my intuition is correct, although the retarded time involves the speed of light, any arbitrary speed will be a valid solution right?

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