Circular motion of an electron in a magnetic field

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Discussion Overview

The discussion revolves around the behavior of an electron in a magnetic field generated by an electric current in a vertical wire. Participants explore the implications of the Lorentz force, the role of the electron's spin, and energy changes associated with circular motion in a magnetic field.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that an electron introduced into the magnetic field will exhibit circular motion due to the Lorentz force, which is described as non-conservative, leading to energy loss over time.
  • Another participant challenges the assumption of circular motion, stating that the magnetic force on a moving charge is not aligned with the magnetic field lines and depends on the initial speed of the electron.
  • Some participants discuss the relationship between the electron's spin and its magnetic properties, questioning why the spin does not influence the Lorentz force when the electron is static.
  • One participant mentions that accelerating charged particles emit radiation, which could account for energy loss, rather than the electron's spin.
  • There is a clarification that the Lorentz force depends on the charge and velocity of the particle, and that spin does not affect linear motion.
  • Another participant notes that the electron's spin is related to its magnetic moment and that it interacts with external magnetic fields, even when not in motion.

Areas of Agreement / Disagreement

Participants express differing views on the role of the electron's spin in relation to the Lorentz force and energy changes. There is no consensus on whether the spin affects the electron's behavior in the magnetic field or on the nature of energy loss during circular motion.

Contextual Notes

Some assumptions about the initial conditions of the electron's motion and the nature of the magnetic field are not fully explored. The discussion includes references to concepts like synchrotron radiation and Larmor radiation without resolving their implications for the scenario presented.

Who May Find This Useful

This discussion may be of interest to those studying electromagnetism, particle physics, or the behavior of charged particles in magnetic fields.

Cathr
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Imagine we take a vertical, infinite wire and we let electric current pass through. The charges create magnetic field all around the wire.

Now if we introduce an electron in the magnetic field, it will have a circular motion around the wire. The Lorentz force is not conservative, this means that there will be a change in the total mechanical energy. After a period, when the particle arrives at the starting point, it will have less energy.

Is this change due to the change in the electron's spin? If so, why does it happen? (We are placing the electron in the vacuum and there is no friction)
 
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Cathr said:
The Lorentz force is not conservative
You are probably thinking about synchrotron radiation or bremsstrahlung. Energy will be carried away in the form of EM radiation.

It has nothing to do with the electron's spin. Accelerating charged particles emit Larmor radiation.
 
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Why do you think that the electron will move around the wire? The magnetic force on a moving charge is not along the magnetic field lines. Magnetic force on a static charge is zero. What the electron does depends on the initial speed (when you "introduce" it).
 
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Thanks a lot!
 
Thanks, this makes sense!
However, one thing that I don't understand is the particle's spin. If it is responsible for the electron's magnetic properties, why doesn't it "feel" the Lorentz force even when it's static?
 
I don't understand your question. The Lorentz force just depends on the charge and the velocity of the particle in an electromagnetic field. The spin doesn't affect the charge of the electron or the linear motion.
 
What I meant is, if spin is giving the particle its magnetic properties, why doesn't it feel the magnetic field even when it's not moving?
 
Cathr said:
What I meant is, if spin is giving the particle its magnetic properties, why doesn't it feel the magnetic field even when it's not moving?
The spin is related to the electron's fundamental magnetic moment (with a gyro-factor around 2, with the deviations from that value being among the best understood quantities of theoretical physics in terms of QED), and as any magnetic moment, there's a force on the electron for inhomogeneous magnetic fields from it (and the spin precesses around the direction of the magnetic field).
 
Cathr said:
why doesn't it feel the magnetic field even when it's not moving?
It does. The electron will interact with an external magnetic field.
 

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