The Lorentz force (2D+3D)

The Lorentz force


See how the Lorentz force can affect a charged particle motion in a uniform magnetic field. For an easy comparison two different particles are shown, with independent parameters but immersed in the same magnetic field (red field lines in the 3D view). In this simulation you can change the particles' velocities x,y,z components, the particles' masses, the particles' initial positions (drag P0 and/or Q0), the particles' charge and the (common) magnetic field magnitude. The uniform magnetic field is fixed in the +z direction. Please note that the electric interaction between the pair of charged particles is not included in this model that is only focused on the Lorentz force. Interesting things to notice and investigate:
  • parameters that actually affects the circular trajectory radius with a direct or inverse proportionality (can you explain why?)
  • parameters that actually affects the particle's speed with a direct or inverse proportionality (can you explain why?)
  • parameters that affects the period T (is it independent from the initial speed? is it independent from the particles' charge to mass ratio (q/m)?)

The 3D view shows that the particle motion can actually be an helical motion if there is a velocity component in the z-direction. In fact the Lorentz force won't act in the z-direction so that the particle will not change its initial velocity along this direction. The global motion will then be a composition of a circular motion (whose parameters are dictated by the initial speed component in the xy plane, the charge, the mass and the magnitude of the magnetic field) with constant speed in the xy plane and a constant velocity motion in the z direction.

The relevant formulas for the circular motion (projection of the global motion in the xy plane) are: radius: time period: