September 2, 1998

PHY 711 - Problem Set # 4

Consider a particle of mass m and charge q moving in a constant magnetic file $\bf{B} = B_0 \bf{\hat{z}}$.

1.

Show that this magnetic field can be described by the vector potential

$$\bf{B} = \frac{1}{2} B_0 ( x \bf{\hat{y}} -y \bf{\hat{x}} ).$$

2.

Write the equations of motion of the particle using cartesian coordinates.

3.

Form the Lagrangian and determine the equations of motion, comparing your results with part (2).