Chapter 10 - How Electric Currents Interact with Magnetic Fields

Abstract

When viewed from a distance, a small current loop is equivalent to a magnet of appropriate strength and orientation. That is, in an external magnetic field, it moves just as its equivalent magnet would move; further, it and its equivalent magnet cause the same force and torque on a distant magnet. This equivalence has extraordinary implications: it enables one to derive all the important results describing how electric currents interact with and produce magnetic fields. Just as a current loop is equivalent to a thin disk-shaped magnet magnetized along its normal (called a magnetic sheet), so a disk-shaped magnet magnetized along its normal is equivalent to a current loop. At large distances from the loop, the details of how the magnetic moment is produced do not matter. However, to make the Ampere approach valid at short distances, we should use the Ampere current loop decomposition into an infinite number of tiny Amperian loops, and replace each loop by a tiny magnet. Consequences of Ampere's Equivalence include torque on a current loop, orientation energy of a current loop, magnetic force on a current-carrying wire, and the force on a charge moving in a magnetic field.