CRT duznt need relativity koz the designers don’t need relativity.
I've shown you how it gets used. You can stick your fingers in your ears and go 'lalalala no it doesn't.' And Steinmetz laughs at you.Anyhow, i am still waiting for u to explain to me how STR can help B' to make an mmf (ie having already used STR to make an mmf from B). No hurry.
Your entire understanding of the phenomena is shoddy 'krapp' so you wouldn't even understand any such answer (if the foundation of your question wasn't even on already super faulty premises). You can't even read the equations.
Let's not forget how little you admit to knowing,I don’t know what STR predicts re fast moving electrons.
Translation:
"Herp dee derp, I don't even know the first thing about relativity."
And you want to get all worked up about relativistic transformations of the E-field in current carrying wires - and you don't even know what a high school AP physics student knows about electrons and special relativity.
This material is too advanced for you. Go back to secondary school. 
Voigt was the first to derive an equation for gamma. But i think it was Searle that was the first to derive a transformation for em radiation. Not for wires, but for em radiation, in connection with length contraction. I think that Lorentz built on that. I think that Larmor used his own transforms to derive equations for gamma for the ticking of atoms. But he didn’t call this time dilation, he wasn’t that stupid. Neither was Lorentz.
But along came Albert, & he was stupid, & he foisted time dilation on the world, & the rest is history.
Anyhow, length contraction is often quite rightly called FitzGerald length contraction.
And ticking dilation is often quite rightly called Larmor ticking dilation. However, this can only apply to atomic clocks, it seems to be fairly accurate re atomic clocks, but its main problem being that it duznt readily explain the change in ticking with elevation. But in any case the Larmor gamma can't be applied to any other kind of clock.
Einstein's STR is based on relative velocity, or in the case of his time dilation it is based on relative speed.
All of the other kinds of relativity are based on the speed of the object through a static aether.
The neoLorentz version is based on the aetherwind blowing through the object or clock.
My own version of relativity is i think the best. The length contraction part is based on neoLorentz. The ticking dilation part is based on a combination of the length contraction due to the aetherwind plus a GTR kind of contribution to the length contraction due to the nearness of mass. All ticking dilation being due to length contraction. With each kind of clock being affected in a different way (eg balance wheel clocks, pendulums etc). I have made an Excel for the ticking dilation of tuning forks.
Bearing in mind that length contraction has never been proven. What i mean is that there is definitely a change in length or in width or some combination, but we don’t know which. I think that Lorentz mentioned this.
The funny thing is that in the modern era the only tests of time dilation have been by using atomic clocks, which were only invented after Einstein died. Einstein loved balance wheel clocks, but (i know that) his time dilation gamma can't possibly apply to balance wheel clocks (but might be ok for atomic clocks)(we don’t know yet).