The Motor Effect states that a current wire placed at a non-zero angle to the lines of force of an external magnetic field experiences a force due to the field. Force due to the motor effect can be calculated with F = BIL. Magnetic Flux Density is the force on 1 meter of wire carrying a current of 1A at right angles to the magnetic field.
A moving charge in a magnetic field experiences a force of F = BQv. This equation can be equated to the centripetal force equation as a magnetic field will apply a perpendicular centripetal force to a moving charged object.
The cyclotron is a particle accelerater which utilises the circular nature of charged objects in a magnetic field. As charged objects cross the dees. an alternating voltage reverses so they are accelerated into the other dee where they are forced on a circular path by a magnetic fiels.