Electron magnetic replusion compared to coulomb attraction

[cragar]

What about starting with an infinite line charge and using gauss's law to find the E field. E=\frac{\lambda}{2\pi r \epsilon_0} 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} B field is in the phi direction.

 

[tris_d]

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:

http://downloads.hindawi.com/archive/1998/079537.pdf

 

[cragar]

I was thinking of the B field created from the motion of the electrons and not their intrinisic dipole moment. Gauss's law would give you a vector.

 

[Vanadium 50]

This thread is rapidly filling with misinformation. Closed.

"...the force of one magnetic dipole on another has not yet been derived in electromagnetism textbooks or the periodical literature."[/I]

Very interesting.

And that's grossly out of context. The authors are discussing a closed-form analytic expression, and by their own admission, what they come up with is an approximation.