Selected bibliography

The reader who is interested in the development of Maxwell's equations from a traditional perspective, beginning with a detailed study of electrostatics and magnetostatics, may choose among several excellent books, such as:

[1-1] Haus, H. A. and J.R. Melcher, Electromagnetic Fields and Energy, Prentice Hall (1989);

[1-2] Jackson, J. D. , Classical Electrodynamics, 2nd edition, Wiley (1975);

[1-3] Panofsky, K. H. and M. Phillips, Classical Electricity and Magnetism, 2nd edition, Addison-Wesley, ((1962);

[1-4] Plonus, M. A., Applied Electromagnetics, Mc Graw-Hill, (1978);

[1-5] Smythe, W. R., Static and Dynamic Electricity, 3rd edition, Mc Graw-Hill (1968); Reprinted by Hemisphere (19 );

[1-6] ]Van Bladel, J., Electromagnetic Fields, McGraw-Hill, (1964). Reprinted by Hemisphere (19 ).

A detailed account is also found in: [1-7] Stratton, J. A., Electromagnetic Theory, McGraw-Hill (1941).

One of the best sources for historical details is the book:

[1-8] Elliott, R. S., Electromagnetics, McGraw-Hill (1966).

Of course, the reader will always profit by consulting the reprint of the classical work by Maxwell:

[1-9] Maxwell, J. C., A treatise on Electricity and Magnetism in two volumes, Dover, (1954)

The connection between circuit theory and electromagnetics is emphasized in:

[1-10] Harrington, R., Time Harmonic Electromagnetic Fields, McGraw-Hill (1961)In the frequency domain, eqs. (1.59) and (1.61) may be rewritten as

$$\nabla^2 \underline{\tilde{E}} + k_0^2 \underline{\tilde{E}}=\und... ... \mu_0 \underline{\tilde{J}}_e + \nabla \times \underline{\tilde{J}}_m \space ,$$ (1.141)

$$\nabla^2 \underline{\tilde{H}} + k_0^2 \underline{\tilde{H}}=\und... ...ilon_0 \underline{\tilde{J}}_m + \nabla \times \underline{\tilde{J}}_e \space ,$$ (1.142)

where the tilde may be dropped if all quantities are interpreted as phasors. With the aid of (1.23), solutions (1.72-1.73) become:

Electromagnetic potentials are discussed in a number of books, such as [1-1], [1-3], [1-6], [1-7] and

[1-11] Jones, D. S., The Theory of Electromagnetism, Macmillan (1964).

In particular, a detailed theory of Hertz vectors and associated gauge transformations is found in:

[1-12] Nisbet, A., ``Hertzian Electromagnetic Potentials and Associated Gauge Transformations'', Proc. Roy. Soc., vol. A231, pp. 250-263 (1955);

see also: [1-13] McCrea, W. H., ``Hertzian Electromagnetic Potentials'', Proc. Roy. Soc., vol. A240, pp. 447-457 (1957).

In a region with sources present, $u$ and $v$ can be expressed in terms of the sources $\underline{\mathcal{J}}_e$ and $\underline{\mathcal{J}}_m$. Read section 7.7 in [1-6], as well as the following two papers:

[1-14] Wilcox, C. H., ``Debye Potentials'', J. Math. Mech., vol. 6, pp. 167-201 (1957).

[1-15] Bouwkamp, C. J., and H. B. G. Casimir, ``On multipole Expansions in the theory of Electromagnetic Radiation'', Physica, vol. 20, pp. 539-554 (1954).