Large amount of electrons rotaing in magnetic feild

[benmww]

I understandthat moving charged particles can be made to rotate in a magnetic field, but what happens when the induced magnetic field of the current exceeds the containing field?

the situation I am imagining is a beta radiation source ejecting high speed electrons perpendiculat to the field. if the source was contiually replace then over time you would have a very large amount of high speed electrons, so what happens to the electrons assuming they all have the same velocity.

additionally, if the electrons have different velocities and so different orbital radii, what is the effect of the magnetic fields on each other?

I don't know much about this sort of stuff so any constructive criticism (and ofcourse explanations) would be appreciated.

 

[GRDixon]

the situation I am imagining is a beta radiation source ejecting high speed electrons perpendiculat to the field. if the source was contiually replace then over time you would have a very large amount of high speed electrons, so what happens to the electrons assuming they all have the same velocity.

This experiment was done many years ago at the Bitter National Magnet Lab in Cambridge, MA. The electrons reportedly go into "quantum" circular orbits, a la the Bohr H atom orbitals. Presumably (Lenz's Law) the magnetic dipole moments of the "orbiting" electrons oppose the external B field.

 

[Bob S]

A typical B field in a cyclotron might be ~ 1 Tesla minimum, so in the magnet gap g

B = μ₀H/g , so

H = Bg/(4 pi x 10^-7) amp turns = 8 x 10⁵ Bg amp turns.

For 1 Tesla and a 20 cm gap, H = 1.6 x 10⁵ amp-turns.

It is hard to imagine 1 amp-turn of beam in a cyclotorn.

So yes, the beam current (like in a betatron) opposes the magnetizing current H, but it is hard to imagine an amp-turn of beam current. In the old 184" cyclotron at Berkeley, the magnet coils (for 2.5 Tesla field and roughly a 50-cm gap) was ~ 2 million amp turns.

Bob S

 

[vin300]

The magnetic field intensifies in the frame of the electron under lorentz transformations, the total is
B`=γB -γ^2(v^2/c^2)B
for v perpendicular to B
(derived from transformation of the Electromagnetic Field Tensor)

 

[sophiecentaur]

Perhaps this effect could be seen to occur in space, where the Earth's field is very low and you get streams of charged particles. Has any distortion of the field been detected (in fact, could it be measured?). Perhaps the streams are very low currents
What about the distortion of the Earth's Magnetic Field around an electrostatically deflected CRT beam? That should qualify as the same effect.