Magnetic Force and the Magnetic Field

As with electric fields, the magnetic field B is defined from a force - in this case the magnetic force:

where q is the particle’s charge and v is the particle velocity. From the definition of cross products, the magnetic force has magnitude

where q is the angle between the velocity and the external magnetic field. Notice that only moving charges experience magnetic forces, and then only if the velocity has a non-zero component transverse to the magnetic field B.