If the velocity of a charged particle moving through a uniform magnetic field has a component parallel to that field the particle will move in a helical path as shown in figure 1. The net force F on the particle can be described by the equation.

F = qvBsin θ

where q is the charge on the particle, v is the velocity of the charge, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. The pitch p of the helix is the distance between adjacent turns. The radius r of the helix is determined by the component of velocity of the charge perpendicular to the magnetic field and is independent of the component of the velocity parallel to the magnetic field. 

Figure 1

A nonuniform magnetic field that is stronger at its ends than at its middle can trap a charged particle by reflecting it back and forth between ends. Such a situation is shown in figure 2.

In a similar phenomenon electrons and protons above the atmosphere are reflected back and forth between the north and south poles of the earth's magnetic field forming the two Van Allen belts high above the atmosphere. Occasionally a solar flare shoots additional electrons and protons into the Van Allen belts. This pushes the electrons to a lesser height. The repulsion due to additional electrons drives the charged particles along the earth's magnetic field lines into the atmosphere where they collide with the air molecules forcing them to a higher energy level emitting photons. Oxygen atoms emit green light and nitrogen atoms emit pink. This light forms the curtain of lights in the sky known in the northern hemisphere as the aurora borealis

----------  Magenetic Field

______  Path of charged particle

Figure 2 : Path of a charged particle trapped in a changing magnetic field