Circular motion of an electron in a magnetic field

[Cathr]

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)

 

[Khashishi]

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.

 

[nasu]

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).

 

[Cathr]

Thanks a lot!

 

[Cathr]

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?

 

[Khashishi]

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.

 

[Cathr]

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?

 

[vanhees71]

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).

 

[Khashishi]

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.