What are the effects of gyromotion on changing magnetic fields?

[TESL@]

Hello,

I am stuck with this problem:
An electron beam is injected perpendicular to a magnetic field. The electrons feel Lorentz force and start to revolve. This movement reduces the magnetic field, therefore the gyroradius gets higher, which in turn increases the magnetic field again. So the electrons again get closer, and they keep oscillating. This seems wrong. I have probably made a wrong assumption.

This also applies to a magnet entering a coil. As the magnetic field strength increases inside the coil, a current is driven "resisting" the increment. So does the field strength remain zero (the magnet is still moving), drop to a constant value, or oscillate like I mentioned above?

Thank you.

 

[TESL@]

up!

 

[Astronuc]

Hello,

I am stuck with this problem:
An electron beam is injected perpendicular to a magnetic field. The electrons feel Lorentz force and start to revolve. This movement reduces the magnetic field, therefore the gyroradius gets higher, which in turn increases the magnetic field again. So the electrons again get closer, and they keep oscillating. This seems wrong. I have probably made a wrong assumption.

There would be some equilibrium. An electric current produces it's own magnetic field. One could calculate a magnetic field due the current of an electron beam and compare the induced field with the applied/imposed external field.

This also applies to a magnet entering a coil. As the magnetic field strength increases inside the coil, a current is driven "resisting" the increment. So does the field strength remain zero (the magnet is still moving), drop to a constant value, or oscillate like I mentioned above?

Thank you.

Lenz's law applies to a magnet moving into a coil (solenoid). There would be backward emf, or counter emf due to the magnetic field of the solenoid current.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c2

When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.

 

[TESL@]

Thanks Astronuc.