The magnetostatic phenomenon is identically like the electrostatic one in its
possession of momentum and energy, and interaction with surrounding objects.
Consequently, the field concept is also fundamental to describe it and understand its
behavior. The sources of the magnetostatic fields are the permanent magnets and
constant electric currents. The essential laws of the magnetostatic fields are Biot-
Savart’s law and Ampere’s law. Biot-Savart’s law is general and applicable to all
current sources, while Ampere’s law is a special case of Biot-Savart’s law and applies
only to specialized problems. In this chapter, Ampere’s law has been introduced first
since it is easier to apply, while Biot-Savart’s law is discussed after the introduction of
the concept of the magnetic vector potential, which is used to derive it. Additionally,
this chapter discusses the concept of magnetic scalar potential, Gauss’s law for
magnetostatic fields, the magnetic force, the magnetic energy, the magnetic dipole, and
the magnetic torque. Moreover, the multi-pole expansion technique is applied to find
the magnetic vector potential and general magnetic fields for some current sources as an
alternative technique. The chapter includes more than twenty examples, ten solved
problems, and numerous illustrative figures, in addition to numerous homework
problems at the end of the chapter.
Keywords: Ampere’s law, Biot-Savart’s law, Gauss’s law for magnetic fields,
magnetic dipole, magnetostatic energy, magnetic force, magnetic scalar potential,
magnetic torque, magnetic vector potential.
