Relativistic momentum through a magnetic field

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SUMMARY

The discussion focuses on the calculation of relativistic momentum in a magnetic field, specifically using the equations p = Bqr and Δp = p Δθ. It establishes that the change in momentum (Δp) is equal to the force (F) applied to the particle multiplied by the time interval (Δt) the particle remains in the magnetic field. This relationship is crucial for understanding the dynamics of charged particles in magnetic fields, particularly in high-energy physics contexts.

PREREQUISITES
  • Understanding of relativistic physics concepts
  • Familiarity with magnetic field interactions
  • Knowledge of basic calculus for momentum calculations
  • Proficiency in vector mathematics
NEXT STEPS
  • Study the Lorentz force law in detail
  • Explore the implications of relativistic effects on particle motion
  • Learn about the applications of magnetic fields in particle accelerators
  • Investigate the mathematical derivation of relativistic momentum
USEFUL FOR

Physicists, students of high-energy physics, and engineers working with particle accelerators will benefit from this discussion on relativistic momentum and magnetic field interactions.

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Homework Statement
A particle with large momentum (relativistic) p , goes through a region with magnetic field 4 tesla
perpendicular to p. The region is 15 cm in length. What is the deflection theta of the particle after it crosses the region.
Relevant Equations
Magnetic field eqation,small angle approximation
p=Bqr and del p = p del theta
 
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\theta=\frac{\triangle p}{p}
where ##\triangle p## is momentum gain from the magnetic field.
\triangle p=F \triangle t
where F is force applied to the particle and ##\triangle t## is time interval when the particle stays in the region.
 

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