I am trying (as an exercise) to determine the force between two wires, in a similar nature to this question here. This suggests a solution based on the wavelength of the wave. However, the wavelength is different in the antenna to that between the antenna - the current is moving at a slower speed in the conductor and to that of light in a vacuum or air.
Wikipedia points out that that the wavelength depends on the Velocity factor of the material (which reduces the velocity to about 70% of the speed of light), which creates a long wavelength. Alternatively, other books/articles, like this here, suggest the velocity (and therefore wavelength) is orders of magnitude lower.
So which wavelength should I use to determine the magnetic field changes along the wire?
Also, if the answer simply turns out that the first is the propagation rate of voltage and the second is the propagation of current, then does that mean that V=IR doesn't work with AC?
EDIT I'm editing the question because I can see a potential misunderstanding of what the question is, when thinking through the lens of the configuration of the referenced question. That was my fault for not being explicit or simple enough with the extraction of my question from out of the details that inspired the question. It may be the case that my question has nothing to do with the wavelength formula given in the referenced question. So here goes my simplification.
If one were to take a snapshot of a wire with an AC running through it, one could assign a current and voltage to every position along the wire, and these follow a sinusoidal function. Therefore it has a wavelength that is associated to the velocity of the wave through the medium. But I have read of two different ways to determine the velocity of the wave through the medium, with very different wavelengths resulting (orders of magnitude different). What is the correct way to calculate the velocity of the wave through the medium, if one wants to measure the (instantaneous elemental) magnetic field along the wire?