# Homework Help: Conservation principles and symmetry; Lagrangian and general momenta problem

1. Mar 3, 2009

### pentazoid

1. The problem statement, all variables and given/known data

A particle of mass m and charge e moves in the magnetic field produced by a current I flowing in an infinte straight wire that lies along the z-axis. The vector potential induced magnetic field is given by

A_r=A_theta=0, A_z=($$\mu$$0*I/2*pi)*ln r, where r , theta, and z are sylindrical coordinates. Find the Lagrangian of the particle. Show that theta and z are cyclic coordinates and find the corresponding conserved momenta

2. Relevant equations

U=e*phi(r)-e*dr/dt*A(r)

L=1/2*m*dr/dt*dr/dt-e*phi(r)+e*dr/dt*A(r)

d/dt*(dT/(dq/dt))-dT/dq=d/dt(dV/(dq/dt))-dV/dq

pj=dL/(dq/dt)

3. The attempt at a solution
U=e*phi(r)-e*dr/dt*A(r)

L=.5*(dz/dt)^2+e*dz/dt*(-$$\mu$$0*I/(2*pi))*ln r

Did I derived the Lagrangian correctly?