## Electron magnetic replusion compared to coulomb attraction

 Quote by cragar What about starting with an infinite line charge and using gauss's law to find the E field. And then figure out what speed the line charges need to move to overcome the force from the E field. $I=\lambda v$ lambda is your charge per lenght. And then use amperes law to find the B field of the moving line charge. $B=\frac{\mu_0\lambda v}{2\pi r}$
Apparently this equation did not exist until 1998, so I guess the derivation is far from trivial. You would need circle instead of line. And since you need vectors instead of Gauss law you would have to use Biot-Savart law and Lorentz force equations, which in other words is Ampere's force law integrated over circle. That's how they did it anyway: