Question

A particle of charge q and rest mass m is moving with velocity v where the magnetic field is B. Here B is perpendicular to v, and there is no electric field. Show that the path of the particle is a curve with radius of curvature R given by R = p/qB, where p is the momentum of the particle, p = mv. (Hint: Note that the force qv × B can only change the direction of the momentum, not the magnitude. By what angle Δθ is the direction of p changed in a short time?)

Name: a particle of charge q and rest mass m is moving with velocity v where the magnetic field is b here b is perpendicular to v and there is no electric field show that the path of the particle 03127
Uploaded: 2023-07-28T17:32:08-08:00
Duration: 1 min 4 s
Channel: Timothy James
Description: a particle of charge q and rest mass m is moving with velocity v where the magnetic field is b here b is perpendicular to v and there is no electric field show that the path of the particle 03127

          A particle of charge q and rest mass m is moving with velocity v where the magnetic field is B. Here B is perpendicular to v, and there is no electric field. Show that the path of the particle is a curve with radius of curvature R given by R = p/qB, where p is the momentum of the particle, p = mv. (Hint: Note that the force qv × B can only change the direction of the momentum, not the magnitude. By what angle Δθ is the direction of p changed in a short time?)

Added by Elizabeth J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

07/28/2023

Step 1

The force acting on the particle is given by the Lorentz force formula: F = q(v × B) Show more…

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A particle of charge q and rest mass m is moving with velocity v where the magnetic field is B. Here B is perpendicular to v, and there is no electric field. Show that the path of the particle is a curve with radius of curvature R given by R = p/qB, where p is the momentum of the particle, p = mv. (Hint: Note that the force qv × B can only change the direction of the momentum, not the magnitude. By what angle Δθ is the direction of p changed in a short time?)