(adsbygoogle = window.adsbygoogle || []).push({}); 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=([tex]\mu[/tex]_{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

p_{j}=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*(-[tex]\mu[/tex]_{0}*I/(2*pi))*ln r

Did I derived the Lagrangian correctly?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**