Magnetostatics Griffiths

[Ramya Bradbury]

ReviewingGriffiths E/M before Jackson is important because it provides a solid foundation for understanding the concepts and principles of classical electrodynamics. Jackson's book builds upon the topics covered in Griffiths, so having a thorough understanding of Griffiths will make it easier to understand Jackson.

Griffiths E/M covers topics such as electrostatics, magnetostatics, electromagnetic induction, Maxwell's equations, and electromagnetic waves. It also includes discussions on electric and magnetic fields, potential, and energy, as well as various applications of these concepts.

Yes, Griffiths E/M is considered to be a beginner-friendly textbook. It presents the concepts in a clear and concise manner, with plenty of examples and exercises to help solidify understanding. It is often used as a textbook for introductory courses in electrodynamics.

Jackson's book, "Classical Electrodynamics," is considered to be a more advanced and comprehensive textbook compared to Griffiths E/M. It covers similar topics but in more depth and also includes advanced topics such as electrodynamics in special relativity and electromagnetic radiation in matter.

It is recommended to read Griffiths E/M cover to cover before starting Jackson. This will provide a solid foundation and understanding of the fundamental concepts before diving into the more advanced topics covered in Jackson's book. However, if you are already familiar with the concepts covered in Griffiths, you can skip to specific chapters in Jackson as needed.

From my understanding, magnetostatics is defined to be the regime in which the magnetic field is constant in time. However, Griffiths defines magnetostatics to be the regime in which currents are "steady," meaning that the currents have been going on forever and charges aren't allowed to pile up anywhere. This part of Griffiths's definition about charges not being allowed to pile up anywhere seems to be placing a constraint on the meaning of magnetostatics that my initial definition doesn't entail. How do you reconcile these (at least ostensibly) not-equivalent definitions? Does charge being locally conserved have something to do with it?

Like all questions about definitions, the answer is not fundamentally "interesting" because, well, it all just boils down to your choice of definitions. But I would define "magnetostatics" to be the regime in which neither the magnetic field nor the electric field depends on time. The motivation for this definition is that the behavior of classical E&M changes very qualitatively (and becomes much more complicated) once the fields become time-dependent, so the regime in which neither field changes over time is a natural one to consider separately.

In this case, Gauss's law for electricity gives that the charge density $\rho$ must be time-independent as well. But then the continuity equation $\bf \nabla \cdot \bf J = -\partial \rho/\partial t$ implies that the current field must be divergence-free. (Conceptually, the subtlety is that if you had steady currents that led to charge piling up, then the charge buildup would create a time-dependent electric field, which would in turn induce another contribution to the magnetic field.)

If you require the current to only be time-independent but not divergenceless, then it turns out that the resulting magnetic field is also constant in time and given exactly by the Biot-Savart law. But you can have steady charge buildup, and the electric field is given by Coulomb's law with the charges evaluated at the present time, not the retarded time - a situation that may appear to, but doesn't actually, violate causality. This is a rather subtle situation, and whether or not you consider it to be "magnetostatic" is a matter of personal preference - but most people probably wouldn't, because even though the magnetic field is constant in time, it still has a contribution from the time-changing electric field via Ampere's law.

Focuses on advanced electro/magnetostatics, such as vector and scalar potentials and multipole expansion of the potential solutions to Laplace's Equation and boundary value problems, as well as time-dependent electrodynamics: Maxwell's Equations, electromagnetic waves, reflection and refraction, wave guides, and generation of electromagnetic radiation (retarded potential). As time permits, topics will be drawn from antennas, relativistic electrodynamics, four vectors, Lorentz, and transformation of fields based on the interest of the class. At the level of Classical Electromagnetic Radiation by Heald and Marion or the more advanced chapters of Introduction to Electrodynamics by Griffiths.

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Description: Electrostatic fields and potentials in vacuum, Gauss' law, electrostatics of dielectrics, magnetostatics, Biot-Savart, Ampere, and Faraday laws, magnetic induction, magnetic materials, and Maxwell's equations.

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