The Wien (E x B) Filter

Developed by E. Behringer

This set of exercises guides the students to compute and analyze the behavior of a charged particle in a spatial region with mutually perpendicular electric and magnetic fields. It requires the student to determine the Cartesian components of hte forces acting on the particle and to obtain the corresponding equations of motion. The solutions to these equations are obtained through numerical integation, and the capstone exercise is the simulation of the E→×B→ (Wien) filter.

Subject Area Electricity & Magnetism
Levels First Year and Beyond the First Year
Available Implementation Python
Learning Objectives

Students who complete this set of exercises will be able to:

  • generate equations predicting the Cartesian components of force acting on the charged particle and generate the equations of motion for the particle (Exercise 1);
  • calculate particle trajectories by solving the equations of motion (Exercise 2);
  • produce two-dimensional and three-dimensional plots of the trajectories (Exercise 2); and
  • simulate the operation of an E→×B→ (Wien) filter (Exercise 3) and determine the range of particle velocities transmitted by the filter, and how these are affected by the geometry of the filter (Exercise 4).
Time to Complete 120 min