Energy of relativistic particle in LHC

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Homework Help Overview

The discussion revolves around the energy of a relativistic particle, specifically a proton in the context of the Large Hadron Collider (LHC). The original poster presents equations related to the motion of the particle and questions the relevance of the proton's mass in their calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to derive expressions for momentum and energy without considering the proton's mass, leading to questions about the validity of their approach. Some participants suggest using the approximation E=pc for energy calculations, while others emphasize the need for relativistic considerations.

Discussion Status

The discussion is active, with participants providing insights into the relevance of mass in relativistic contexts and clarifying the use of specific equations. There is acknowledgment of the original poster's equations, but also a caution regarding their applicability to relativistic particles.

Contextual Notes

Participants note that the original poster's equations may be more suited for nonrelativistic scenarios, and there is a mention of inaccuracies in a provided sketch related to LHC components.

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Homework Statement


(see attachment)
The proton charge is ##1.6 \times 10^{-19} C## and the speed of light is ##3 \times 10^8 m/s##. The proton's mass is not necessary in this problem.


Homework Equations





The Attempt at a Solution


The particle revolves in a circular path, hence
[tex]\frac{mv^2}{R}=qvB[/tex]
[tex]mv=eRB[/tex]
(e is the charge of particle)
Since p=mv (momentum)
[tex]p=eRB[/tex]
I don't understand how the mass of proton is not necessary for the problem. Is my expression for p correct?

Any help is appreciated. Thanks!
 

Attachments

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    lhc.png
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Your equations do not use the proton mass, how could it be relevant? You can use the approximation ##E=pc## to get the energy, as the mass of the proton is negligible relative to its momentum.

Your formulas are good for nonrelativistic particles only, you cannot use this approximation for protons in the LHC.
The result is the same with relativistic formulas, but that is just a coincidence here.

The sketch has wrong positions for LHCb and ALICE :(.
 
mfb said:
Your equations do not use the proton mass, how could it be relevant? You can use the approximation ##E=pc## to get the energy, as the mass of the proton is negligible relative to its momentum.

Your formulas are good for nonrelativistic particles only, you cannot use this approximation for protons in the LHC.
The result is the same with relativistic formulas, but that is just a coincidence here.

The sketch has wrong positions for LHCb and ALICE :(.

Thanks a lot mfb for the help! :smile:
 
Pranav-Arora said:
1. I don't understand how the mass of proton is not necessary for the problem. Is my expression for p correct? p=eRB


Yes it is, even relativistically, if you remember p is the relativistic momentum = mv = γm0v.
 

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