Charge moving in cyclotron orbit

AI Thread Summary
The discussion focuses on determining the angular frequency (omega) of a charged particle moving in a cyclotron orbit within a magnetic field. The relationship between the forces acting on the particle, including the magnetic force and the centripetal force, is explored to derive omega in terms of charge (q), mass (m), and magnetic field strength (B_0). The equations F = q(v X B) and F = (m*v^2)/r are central to the analysis. Additionally, there is a request for the Lagrangian of the system expressed in plane polar coordinates. The conversation emphasizes the interplay between magnetic fields and circular motion dynamics.
tarellan
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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
 
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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.
 
can anyone give the Lagrange of the system in plane polar coordinates?
 

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