See how the Lorentz force [math]F_L=q\vec{v}\otimes\vec{B}[/math] can affect a charged particle motion in a uniform magnetic field. [br]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).[br]In this simulation you can change the particles' velocities x,y,z components, the particles' masses, the particles' initial positions (drag [i]P[sub]0[/sub][/i] and/or [i]Q[sub]0[/sub][/i]), the particles' charge and the (common) magnetic field magnitude.[br][br]The uniform magnetic field is fixed in the +z direction.[br][b]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.[/b][br][br]Interesting things to notice and investigate:[br][list][*]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 [i]T[/i] (is it independent from the initial speed? is it independent from the particles' charge to mass ratio ([i]q[/i]/[i]m[/i])?)[/*][/list][br][justify]The 3D view shows that the particle motion can actually be an [i]helical[/i] motion if there is a velocity component in the [i]z[/i]-direction. In fact the Lorentz force won't act in the [i]z[/i]-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 [i]xy[/i] plane, the charge, the mass and the magnitude of the magnetic field) with constant speed in the [i]xy[/i] plane and a constant velocity motion in the [i]z[/i] direction.[/justify][br][br]The relevant formulas for the circular motion (projection of the global motion in the [i]xy[/i] plane) are:[br]radius: [math]r=\frac{mv_{xy}}{qB}[/math][br]time period: [math]T=2\pi\frac{m}{qB}[/math][br][br]