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**From electrostatics to optics: a concise electrodynamics course.**
*(English)*
Zbl 0807.35140

Texts and Monographs in Physics. Berlin: Springer-Verlag. viii, 255 p. (1994).

The book, notwithstanding its title ‘From Electrostatics to Optics’, is a concise course on classical electrodynamics, from modern perspective. It begins with a historical introduction and mathematical preliminaries, in which the topics are judicously chosen to present the book effectively as a self-contained one.

It begins with electrostatics in vacuum, starting with Gauss’ law, followed by multipole expansion and boundary value problems and energy of the electric field. A conspicuous difference of the book from other literature in this field is its attempt to derive Maxwell’s equations in vacuum from electrostatics and the Lorentz transformations of the special theory of relativity, through the Lorentz force. (A part of the latter is due to magnetic field, which appears to have been introduced in an ad hoc manner. This seems to be the price one has to pay to introduce the Maxwell equations, before formal introduction of magnetic field.)

The important role of the fundamental laws, such as Faraday’s law of induction, Lenz’ law, Ampère’s law and the Biot-Savart law are discussed as consequences of Maxwell’s equations. This is noteworthy as most modern literature rarely mention about them.

Stationary magnetic fields are considered as special cases of Maxwell’s equation, in the chapter on electrodynamics in vacuum. In this chapter the electromagnetic radiation, its production, electromagnetic potential and the electromagnetic fields of moving charges are discussed in detail. It also contains the Lagrangian formalism of electrodynamics in brief.

The subject of phenomenological electrodynamics of matter is taken up in the next chapter. The phenomenological equation are obtained by spatial averaging, assuming a classical model for the atomic structure of matter. It contains brief discussions on the electrodynamics of superconductors and the Cěrenkov radiation.

Finally, in the chapter on optics, the fundamental laws of geometrical and wave optics, light scattering, diffraction theory and the classical theory of laser are developed as applications of the phenomenological electrodynamics. The relations of the classical electrodynamics to modern quantum electrodynamics is very briefly incorporated in an epilogue.

Each chapter of the book is supplemented with a good number of important and very instructive problems. It may be used as a good text book for advanced students in general, though it is addressed to students of theoretical physics.

It begins with electrostatics in vacuum, starting with Gauss’ law, followed by multipole expansion and boundary value problems and energy of the electric field. A conspicuous difference of the book from other literature in this field is its attempt to derive Maxwell’s equations in vacuum from electrostatics and the Lorentz transformations of the special theory of relativity, through the Lorentz force. (A part of the latter is due to magnetic field, which appears to have been introduced in an ad hoc manner. This seems to be the price one has to pay to introduce the Maxwell equations, before formal introduction of magnetic field.)

The important role of the fundamental laws, such as Faraday’s law of induction, Lenz’ law, Ampère’s law and the Biot-Savart law are discussed as consequences of Maxwell’s equations. This is noteworthy as most modern literature rarely mention about them.

Stationary magnetic fields are considered as special cases of Maxwell’s equation, in the chapter on electrodynamics in vacuum. In this chapter the electromagnetic radiation, its production, electromagnetic potential and the electromagnetic fields of moving charges are discussed in detail. It also contains the Lagrangian formalism of electrodynamics in brief.

The subject of phenomenological electrodynamics of matter is taken up in the next chapter. The phenomenological equation are obtained by spatial averaging, assuming a classical model for the atomic structure of matter. It contains brief discussions on the electrodynamics of superconductors and the Cěrenkov radiation.

Finally, in the chapter on optics, the fundamental laws of geometrical and wave optics, light scattering, diffraction theory and the classical theory of laser are developed as applications of the phenomenological electrodynamics. The relations of the classical electrodynamics to modern quantum electrodynamics is very briefly incorporated in an epilogue.

Each chapter of the book is supplemented with a good number of important and very instructive problems. It may be used as a good text book for advanced students in general, though it is addressed to students of theoretical physics.

Reviewer: N.D.Sengupta (Bombay)

### MSC:

35Q60 | PDEs in connection with optics and electromagnetic theory |

78-02 | Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory |

00A79 | Physics |