28.2 : Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.

A magnetic field is defined by the force that a charged particle experiences moving in that field. The magnitude of this magnetic force is proportional to the amount of charge, Q, the speed of the charged particle, v, and the magnitude of the applied magnetic field, B. The direction of this force is perpendicular to both the direction of the moving charged particle and the direction of the applied magnetic field. Based on these observations, we define the magnetic field strength based on the magnetic force on a charge, Q, moving at a certain velocity as the cross-product of the velocity and the magnetic field:

This equation defines the magnetic field with respect to the force on the motion of a charged particle. The magnitude of the force is determined from the definition of the cross-product as it relates to the magnitudes of each of the vectors. In other words, the magnitude of the force satisfies the following equation:

where θ is the angle between the velocity and the magnetic field.

The SI unit for magnetic field strength is called the tesla (T) after the eccentric but brilliant inventor Nikola Tesla (1856–1943):

A non-SI magnetic field unit in common use is called the gauss (G) and is related to the Tesla through the following conversion:

There is no magnetic force on static charges. However, there is a magnetic force on charges moving at an angle to a magnetic field. When charges are stationary, their electric fields do not affect magnets. However, when charges move, they produce magnetic fields that exert forces on other magnets. When there is relative motion, a connection between electric and magnetic forces emerges, with each affecting the other.