# Magnetic field of gyromotion

• TESL@
In summary, the conversation discusses the concept of Lorentz force and its effect on the movement of electrons in a magnetic field. The speaker also raises a question about the behavior of a magnet entering a coil and the application of Lenz's law. They mention the possibility of an equilibrium and the calculation of the induced magnetic field. The responder adds that Lenz's law also applies to a magnet moving into a coil, causing a counter emf.

#### 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.

up!

TESL@ said:
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.

• vanhees71
Thanks Astronuc.

## 1. What is the magnetic field of gyromotion?

The magnetic field of gyromotion refers to the magnetic field that is generated by a moving charged particle as it rotates or orbits around a central axis. This field is perpendicular to both the particle's velocity and the axis of rotation, and its strength is dependent on the particle's velocity, charge, and mass.

## 2. How is the magnetic field of gyromotion calculated?

The magnetic field of gyromotion can be calculated using the formula B = qv/r, where B is the magnetic field strength, q is the charge of the particle, v is its velocity, and r is the radius of its orbit. This formula is known as the Lorentz force law and is a fundamental principle in electromagnetism.

## 3. What is the significance of the magnetic field of gyromotion?

The magnetic field of gyromotion plays a crucial role in many physical phenomena, such as the motion of charged particles in a magnetic field, the behavior of plasma in fusion reactors, and the formation of celestial bodies like planets and stars. It also has practical applications in technologies such as particle accelerators and MRI machines.

## 4. How does the magnetic field of gyromotion affect charged particles?

The magnetic field of gyromotion can exert a force on charged particles, causing them to change direction and follow a curved path. This phenomenon is known as the Lorentz force and is responsible for the circular motion of particles in a magnetic field. The strength and direction of the force depend on the charge, velocity, and orientation of the magnetic field.

## 5. Can the magnetic field of gyromotion be manipulated?

Yes, the magnetic field of gyromotion can be manipulated by changing the velocity, charge, or direction of the moving charged particles. It can also be altered by adjusting the strength and orientation of external magnetic fields. This manipulation is essential in controlling and studying the behavior of particles in various scientific and technological applications.