12.4: Magnetism and Moving Charges

• A single moving charged object produces a magnetic field.

• The magnetic field produced by a moving charged object is directly proportional to the magnitude of charge and the object’s velocity and inversely proportional to the square of the distance from the object.

• The direction of the magnetic field at a point in space produced by a moving point charge is perpendicular to both the velocity of the point charge and the position vector from the point charge to that point in space and can be determined using the right-hand rule.

Magnetic forces describe interactions between moving charged objects.

A magnetic field may exert a force on a charged object moving within that field.

• The magnitude of the force exerted by the magnetic field on a moving charged object is proportional to the magnitude of the charge, the magnitude of the charged object’s velocity, and the magnitude of the magnetic field, and depends on the angle between the velocity and magnetic field vectors.

• The direction of the force exerted by a magnetic field on a moving charged object is perpendicular to both the direction of the magnetic field and the velocity of the charge, as defined by the right-hand rule.

In a region containing both a magnetic field and an electric field, a moving charged object will experience independent forces from each field.

The Hall effect describes the potential difference created within a conductor in an external magnetic field that has a component perpendicular to the direction of charges moving in the conductor.

If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor. This is most evident in a thin flat conductor as illustrated. A buildup of charge at the sides of the conductors will balance this magnetic influence, producing a measurable voltage between the two sides of the conductor.