A charged particle will induce a magnetic field as it moves perpendicular to its direction of motion. This magnetic field is a vector quantity and hence can have two directions along one plane, moving to the left of the motion and moving to the right of the motion. If an external magnetic field is present in the same plane as the induced field (i.e. when it is at right angles to the direction of motion) the two magnetic fields will interact to produce regions of high magnetic density and low magnetic density (when the fields are pointing in the same direction they will add and grow stronger, when they are pointing in opposite directions they will cancel and grow weaker). This interaction will result in high magnetic pressure on one side of the charged particle and low magnetic pressure on the other side, resulting in a "catapulting" of the particle into the region of lower magnetic density. The deflection is a force known as an electromotive force, or the motor effect.
Calculating the Size and Direction of the Force
The size of the force is given by Felectromotive = qvB(sinX) where q = charge on the particle (coulombs), v = velocity of the particle (ms−1), B = magnetic field density (tesla) and X = angle between field and direction of the charge (only the vector component of the particle perpendicular to the field will produce the force).
The direction of the force on a positively charged particle can be easily obtained using the right hand push rule (this avoids mapping the interaction between the fields). The right hand is held with the palm pointing away from the body as if pushing the air, the fingers point to the sky and the thumb points to the left (i.e. at a right angle to the fingers). The direction of the magnetic field is represented by the fingers, the velocity of the particle is represented by the thumb and the force of deflection on the particle is the direction the palm is facing (i.e. away from the body). This setup can then be orientated to suit any situation. If the charged particle is negatively charged the left hand can be used.
The motor effect is the principle on which all electric motors are built. As a conductor is a flow of electrons (negatively charged particles) a wire can be placed in a magnetic field and deflected. If many wires are placed in the field and tied together the overall deflection on them will be greater (the increase in force outweighs the increase in mass, hence the acceleration will increase). This has developed into the coils we see in everyday motors.
The motor effect is also utilised in a variety of other applications such as cathode ray tubes in televisions (in many rear screen projectors electromagnets are used in the deflection system), in electron microscopes (electromagnets are used to accelerate electrons), in loudspeakers (a coil is wrapped around a magnet, the alternating current in the coil causes it to be deflected in and out producing sound waves) and in galvanometers.