Motion of Charged Particles in Magnetic Field

 The magnetic force on a charge q moving with vector velocity v in a magnetic field is described by the formula F = qvBsinα, where α is the angle between the vectors v and B. The direction of the magnetic force is always perpendicular to the velocity of the particle. Note that the force can only change the direction of the particle's velocity, and not its magnitude. The magnetic force cannot do work on the particle. If the direction of the particle's vector velocity v in a uniform magnetic field is perpendicular to the vector B, the particle moves with a constant speed and its trajectory is a circle of the radius R = mv/qB. If the direction of the initial velocity is not perpendicular to the vector of field B, the velocity component parallel to the field is constant, and the particle moves in a helix. At the same time, in the plane that is perpendicular to the field, the particle's trajectory is a circle. The period of one cycle is T = 2πR/v = 2πm/qB and it is independent from the particle?s speed.