I Simple electromagnetic wave including delay

AI Thread Summary
The discussion focuses on deriving the electric and magnetic fields around an infinitely long wire carrying a sinusoidal alternating current, emphasizing the inclusion of phase delay due to the finite speed of wave propagation. The velocity of the sinusoidal wave is crucial for determining the field pattern, particularly in sub-luminal conductors where energy primarily propagates in the sinusoidal direction. It is noted that this problem has been addressed over a century ago, suggesting that existing literature may provide the necessary insights. A specific reference to the paper by Beverage, Rice, and Kellogg is recommended for further understanding. The conversation underscores the importance of consulting established sources in electromagnetic theory for such derivations.
a1titude
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$E(r,t)$ and $H(r,t)$ around $I*\sin(2*pi*f*t)$
I want to derive the electric and magnetic field at a point around an infinitely long wire which carries a sinusoidal alternating current. And I want the answer includes the phase delay according to the limited speed of propagation of the wave. Surely the answer must satisfy the Maxwell's equations. I have never seen such answers from anywhere yet. Please, someone derive them for me or recommend me some references.
 
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Look at the sections 8.2-8.3 on retarded potentials in Stratton, Electromagnetic Theory.
 
a1titude said:
And I want the answer includes the phase delay according to the limited speed of propagation of the wave.
That is a type of travelling wave antenna, but with an infinite length wire.

The velocity of the sinusoid propagating along the wire is critical in determining the field pattern.
For sub-luminal conductor propagation, (with insulation or oxide), most of the energy is launched in the direction the sinusoid is propagating along the conductor, the conductor forward of there, can often be discounted.

The problem was solved over 100 years ago. You have obviously been reading the wrong books and papers.

This paper, by Beverage, Rice and Kellogg, is well worth reading at breakfast.
https://www.crosscountrywireless.net/The Wave Antenna.pdf
 
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