Perfectly elastic collision between two electrons in ⊥ B-field

AI Thread Summary
The discussion centers on the dynamics of perfectly elastic collisions between electrons in a perpendicular magnetic field. Participants debate the exclusion of electrical potential energy in the conservation of energy calculations, suggesting it may be negligible due to the short time interval involved. There is clarification on the internal structure of electrons, with consensus that they are considered elementary particles, unlike protons which contain quarks. The conversation also touches on the potential for energy loss during collisions due to electromagnetic radiation, although this is deemed negligible for the problem at hand. Overall, the focus remains on the assumptions made in analyzing the elastic collision scenario.
member 731016
Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1673752127546.png

The solution is,
1673752152479.png

However, is the reason why they don't include electrical potential energy because the time interval for which we are applying conservation of energy over is very small so the change in electric potential energy is negligible?

Also, when they said, "electrons have no internal structure to absorb energy", would it not be more concise to say "The internal structure of electrons cannot absorb kinetic energy"?

My statement reflects that electrons do have internal structure consist of quarks which can absorb and emit energy by via photonic emission.

Many thanks!
 
Physics news on Phys.org
And even it it where protons in this problem, you can assume that there is no change in their internal energy because we need quite high energy to change the quark configuration in them. If electrons have subparticles (preons or whatever) we still assume that the energies involved in this problem is not large enough to resolve that. It is written in the problem that they undergo elastic collision. Thus, there is no change in internal energy.
 
Last edited:
  • Like
Likes member 731016
malawi_glenn said:
And even it it where protons in this problem, you can assume that there is no change in their internal energy because we need quite high energy to change the quark configuration in them. If electrons have subparticles (preons or whatever) we still assume that the energies involved in this problem is not large enough to resolve that. It is written in the problem that they undergo elastic collision. Thus, there is no change in internal energy.
Thank you for your help @malawi_glenn !
 
Callumnc1 said:
However, is the reason why they don't include electrical potential energy because the time interval for which we are applying conservation of energy over is very small so the change in electric potential energy is negligible?
The final radii are measured when the electrons are far apart - so their potential energy is zero. You are determining the kinetic energy of the incident electron when the initial separation was large, so the intial potential energy was also zero. (The question could have been a bit clearer about this!)

FWIW, although electrons have no internal structure, that does not mean electron-electron collisions are necessarily elastic. Loss of (kinetic) energy can occur due to the production of EM radiation. For example that’s how an X-ray tube produces X-rays – ‘bremsstrahlung’. But you can assume the effect is negligible in this question, because you are told the collision is elastic.
 
  • Like
Likes member 731016
Steve4Physics said:
The final radii are measured when the electrons are far apart - so their potential energy is zero. You are determining the kinetic energy of the incident electron when the initial separation was large, so the intial potential energy was also zero. (The question could have been a bit clearer about this!)

FWIW, although electrons have no internal structure, that does not mean electron-electron collisions are necessarily elastic. Loss of (kinetic) energy can occur due to the production of EM radiation. For example that’s how an X-ray tube produces X-rays – ‘bremsstrahlung’. But you can assume the effect is negligible in this question, because you are told the collision is elastic.
Ok thank you for your help @Steve4Physics !
 
Back
Top