Magneto: Magnetostatics

  • Zhen (Leo) Liu


The study of the magnetic field originated from the observations on the magnets and the forces they place on objects made of iron and other metals. The study of these phenomena, i.e., magnetism, has extended far beyond magnets and has been entangled with the study of the electric field in electromagnetics. In this chapter, we will first discuss the forces associated with a charge in a magnetic field to introduce the concept of the magnetic field (B field), just like what we did in the previous chapter for the electric field. Then, we will present a mathematical description of the magnetic field using two different methods relying on the H field and B field. Gauss’s law for magnetism will be given to reach the governing equation for the magnetic field. A vector potential will be introduced to turn the governing equation into a second-order partial differential equation, which is useful and common in numerical analysis. The energy associated with the magnetic field will be introduced afterward. A practice problem will be provided in the final section for simulating the magnetic field generated by a permanent magnet.


Magnetostatics Magnetic field Magnets H field B field Gauss’s law for magnetism Magnetic vector potential Magnetostatic energy 

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Zhen (Leo) Liu
    • 1
  1. 1.Michigan Technological UniversityHoughtonUSA

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