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Homework Help: Lagrangian for a particle in a uniform magnetic field

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data
    We know that for a uniform static magnetic field, we may take
    V = 0, A = 1/2 B x r (vector potential)

    Now, I have to write the Lagrangian L in cylindrical coordinates, but I'm not sure I'm doing it right and this goes on for hours now, so maybe someone can help me out.

    2. Relevant equations

    3. The attempt at a solution
    I found [tex]L = 1/2 m ( \dot{r}^2 + r^2 \dot{\phi}^2 + \dot{z}^2 ) + 1/2 q ( ( B_{\phi} z - B_{z} \phi ) \dot{r} + ( B_{z} r - B_{r} z ) r \dot{\phi} + ( B_{r} \phi - B_{\phi} r ) \dot{z} ) ) [/tex]

    Is this correct?
  2. jcsd
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