Direction of a particle in a uniform magnetic field.

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SUMMARY

The discussion focuses on the motion of a particle in a uniform magnetic field, specifically analyzing the displacement of a particle with velocity vector v as it enters a magnetic field B in the +x direction. It establishes that the x component of the displacement can be expressed as 2 * Pi * (m / qB) * vcos(theta), where theta is the angle between the velocity vector and the magnetic field vector. The period of circular motion is confirmed to be T = 2 * Pi * m / q * B, indicating that the particle's velocity remains directed as it was upon entering the field.

PREREQUISITES
  • Understanding of classical mechanics, specifically circular motion.
  • Familiarity with the Lorentz force and its effects on charged particles.
  • Knowledge of vector notation and trigonometric functions.
  • Basic principles of electromagnetism, particularly magnetic fields.
NEXT STEPS
  • Study the derivation of the Lorentz force equation for charged particles in magnetic fields.
  • Learn about the implications of the right-hand rule in determining particle motion in magnetic fields.
  • Explore the concept of cyclotron motion and its applications in particle accelerators.
  • Investigate the effects of varying magnetic field strengths on particle trajectories.
USEFUL FOR

Students of physics, particularly those studying electromagnetism and mechanics, as well as educators seeking to clarify concepts related to particle motion in magnetic fields.

nvictor
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Homework Statement



a beam of particles with velocity v^vector enters a region that has a uniform magnetic field B^vector in the +x direction.

show that when the x component of the displacement of one of the particles is 2 * Pi * (m / qB) * vcos(theta), where theta is the angle between v^vector and B^vector, the velocity of the particle is in the same direction as it was when the particle entered the field

Homework Equations



the period of circular motion is T = 2 * Pi * m / q * B

The Attempt at a Solution



if I divide v = d * t = x * t

if I choose t to be T then I find v = v cos(theta).

then thing is, I don't really undertstand the question, and I want to know how to proceed from there.
 
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Hi nvictor! :smile:

(have a theta: θ and a pi: π and use bold for vectors :wink:)
nvictor said:
show that when the x component of the displacement of one of the particles is 2 * Pi * (m / qB) * vcos(theta), where theta is the angle between v^vector and B^vector, the velocity of the particle is in the same direction as it was when the particle entered the field

The displacement in the x-direction is (vcosθ)t (because speed in that direction is constant), so the question is asking you to prove that the period is 2πm/qB :smile:
 
thanks a lot for the reply.
 

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