Magnetostatic Fields

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.