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Charge moving in cyclotron orbit

  • Thread starter tarellan
  • Start date
  • #1
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Homework Statement



The particle moves in a plane perpendicular to the magnetic field direction as shown in the figure. What is omega, the angular frequency of the circular motion?

Express omega in terms of q, m, and B_0.


Homework Equations


32439.jpg


omega=2pi/T

The Attempt at a Solution



I found that At a given moment the particle is moving in the +x direction (and the magnetic field is always in the +z direction). If q is positive, the direction of the force on the particle due to the magnetic field is -y direction
 

Answers and Replies

  • #2
12
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The force on a charged particle in a Magnetic Field B is given by F = q(v X B).

The force required to accelerate a particle of velocity v in a circular motion is related to the radius of the circular path and the mass of the particle by F=(m*v^2)/r

Omega can also be expressed as v/r.

By equating the two forces and playing around a bit i'm sure you'll come out with your answer.
 
  • #3
2
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can anyone give the Lagrange of the system in plane polar coordinates?
 

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