We all know what is the speed of an electromagnetic wave.
But I want to know the speed at which the electrostatic field or the magnetostatic field spreads in the space.
An electrostatic field cannot spread - it is static. There has been no electrostatic field in the history of the universe and there never will be. All fields have started, and may stop. This means that are not static. They may be very low frequency - in your lab they may be 1/1 day frequency, or 1/1 minute. The rate of spread can be calculated for the frequencies in the signal calculated using the frequency content of the change, that can be calculated using Laplace or Fourier transforms. When you switch it on it may reach full strength in 1 second so will have a strong signal near 1/2 Hz, which propagates out at the speed of light. As you leave it on longer, this 1/2 Hz signal dies away and progressively lower levels of progressively lower frequencies take over, but they are not static. The result approaches an electrostatic or magnetostatic result the longer it is left unchanged.
What is harder to understand is the change in near-fields, of radiators, which appears to me to be instantaneous, as quantum tunnelling or other quantum things. However, instantaneous is a difficult concept in a world where people travelling at different speeds don't agree that events at two different places are simultaneous. So I hope to understand all of this better in the future!
“What is the speed at which the electrostatic field can spread?”
- that electrostatic field spreads with the speed of light is introduced in classical electrodynamics yet in ~1900 year after Liénard and Wiechert works. And that is really so – electric field [and magnetic field, which really is some transformation of electric field] are flows of fundamental Nature Electric force mediators, which are specific disturbances in the Matter’s ultimate base
– the (at least) [4+4+1]4D dense lattice of the primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which [the lattice] is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),
- and so all disturbances, including fundamental Nature forces mediators, which [of at least Gravity, Electric, and Nuclear Forces propagate in 3DHYZ space], propagate in the space having the speed c that is determined by main FLE parameters – “FLE size” and “FLE binary flip time”, which are equal to Planck length and Planck time, lP and tP, c=lP/tP.
More see the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in
https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces
Cheers
This kind of questions and examples are sometimes used to "visualize" claimed superluminal propagation..at best you can visualize superluminal phase velocities which exist in any hollow waveguide ..or just the movement of the light dot from a laser pointer going over the moon (if you could see it)
we have two different types of speed
electrostatics and field
Coulomb's Law describes forces acting at a distance between two charges. , using an electric field.
your equation has two different questions at work here kind of mixed together.
The first question is
"What is the speed at which a change in the electric field propagates?"
The answer to that is the speed of light the electromagnetic interaction that we see as the electric field is mediated by photons, so any change in an established field (say, due to shifting the position of the charge creating the field).
The second question is
"What is the speed of propagation of electric current?"
This speed is slower than the speed of light, but still on about that order of magnitude and the value depends a little on the arrangement of transfer media and so on.
relativity tells us that no information can travel faster than tell speed of light.
That is the disturbance of a typical electric field can only travel slower than the speed of light.
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