Uniform circular motion for proton and 2 particles

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SUMMARY

The discussion focuses on calculating the kinetic energy of two particles moving in a uniform magnetic field on a circular orbit, based on the kinetic energy of a proton. The kinetic energy of the proton is expressed as Kp = 1/2 (e^2B^2r^2/u). For particle 1, with charge q=+e and mass m=2u, the kinetic energy is K = Kp/2. For particle 2, with charge q=+2e and mass m=4u, the kinetic energy equals Kp. The calculations confirm that the energy relationships are correct based on the principles of uniform circular motion.

PREREQUISITES
  • Understanding of kinetic energy equations, specifically K = 1/2 mv^2
  • Familiarity with the principles of uniform circular motion in magnetic fields
  • Knowledge of charge and mass relationships in particle physics
  • Basic understanding of magnetic field effects on charged particles
NEXT STEPS
  • Study the derivation of kinetic energy in magnetic fields for charged particles
  • Explore the Lorentz force and its impact on particle motion
  • Learn about the implications of varying mass and charge on kinetic energy calculations
  • Investigate applications of uniform circular motion in particle accelerators
USEFUL FOR

Students and educators in physics, particularly those focusing on electromagnetism and particle dynamics, as well as anyone interested in the behavior of charged particles in magnetic fields.

cseil
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[Note by mentor: This thread does not use the homework template because it was moved here from a non-homework forum.]

Hello,
I have a problem with this exercise. I don't know if my solution is right! Could you check it, please?

A proton with kinetic energy Kp is moving in a uniform magnetic field on a circular orbit.
I have to calculate the energy of two particles moving on the same orbit knowing that:
particle 1 : q=+e, m=2u
particle 2: q=+2e, m=4u

Kp = 1/2 mv^2
v = qBr/m (uniform circular motion).

So

Kp = 1/2 q^2B^2r^2/m

proton: Kp = \frac{1}{2} \frac{e^2B^2r^2}{u}

particle 1: K = \frac{1}{2} \frac{e^2B^2r^2}{2u} = Kp/2

particle 2: K = \frac {1}{2} \frac{4e^22B^2r^2}{4u} = Kp

Is that right?
Thank you
 
Last edited by a moderator:
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Yes, I think it is right.
 
Thank you.
I'm sorry but I didn't see the Homework section, won't happen again!
 

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