Perfectly elastic collision between two electrons in ⊥ B-field

In summary, the conversation discusses the inclusion of electrical potential energy in a problem involving conservation of energy, and the reason for its exclusion due to the negligible change in potential energy over a small time interval. There is also a clarification on the internal structure of electrons and the potential for energy loss in elastic electron-electron collisions. The final radii in the problem are measured when the electrons are far apart, resulting in zero potential energy.
  • #1
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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!
 
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  • #4
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.
 
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  • #5
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 !
 
  • #6
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.
 
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  • #7
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 !
 
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