# Lagrangian for a particle in a uniform magnetic field

1. Sep 19, 2009

### mwoerden

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
$$\frac{d}{dt}\frac{dL}{d\dot{q}}=\frac{dL}{dq}$$

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

Is this correct?