ACollierAstro: electricity and magnetism are the same thing at https://www.youtube.com/watch?v=-nxyriaA2UQ
At low speeds. 1/sqrt(1-v^2/c^2) = (1/2)*v^2/c^2. From your derivation you used mostly things where that is likely. There are many derivations of the same equivalence between electricity and magnetism where they use the Lorentz transformation and the charge velocity is any size, except near the speed of light. The speed of light and gravity are identical. Not close, identical. I was trying to calculate the time dilation effects at walking speeds and the floating point calculators all fail. So I asked ChatGPT to check me on the Taylor series expansion of 1/sqrt(1-v^2/c^2). Check me, it has been a long day and I am writing from memory, not my notes. I seem to remember the electron velocity was in micrometers per second. But I will go back and do it later. It is slower than about 10 meters/second where the Lorentz gamma simply won’t calculate with 64 bit floating point.. When an electron goes for a walk, the magnetic field she produces is going down into the ground on her right. The positive charge walking beside her, his magnetic field is going down into the ground on his left. I hate right hand rules; I am 74 now and have hated them for 6 decades. But is it easy to remember an electron’s right hand, as she walks.