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.

 

[sardar]

Hello there,

It appears that you are referring to the phenomenon known as gyromotion, where a charged particle moves in a circular path due to the combination of a magnetic field and a perpendicular velocity. It is a common misconception that the gyromotion of an electron reduces the magnetic field, but in reality, it is the changing magnetic field that causes the electron to gyrate. This is known as the self-induction effect.

In the case of an electron beam injected perpendicular to a magnetic field, the Lorentz force causes the electrons to move in a circular path, which in turn changes the magnetic field. However, this change in the magnetic field is not enough to completely cancel out the original field, and so the electrons continue to oscillate around the center of the field.

As for the scenario of a magnet entering a coil, the magnetic field inside the coil will indeed increase, and this will induce a current in the coil that opposes the change in the magnetic field. This is known as Lenz's law. The resulting current will create its own magnetic field that will interact with the original magnetic field, causing it to decrease. This process will continue until the magnet reaches the center of the coil, at which point the magnetic field inside the coil will be constant.

I hope this helps to clarify your understanding of gyromotion and the effects of changing magnetic fields. If you have any further questions or concerns, please don't hesitate to ask. As scientists, it is important to question and analyze our assumptions in order to better understand the phenomena we are studying. Keep up the good work!