Electromagnetic Theory
Julius Adams Stratton
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Stratton's is the textbook that fixed the working practice of building electromagnetic fields out of potentials rather than out of the field vectors themselves, and it is still the standard reference for the technique. The chapter that matters here introduces the Hertz vectors, which Stratton also calls the polarization potentials: having already reduced Maxwell's equations to a vector and a scalar potential obeying the same differential equation, he shows, following Hertz, that in ordinary conditions the whole electromagnetic field can be defined in terms of a single vector function instead. Later, for problems with boundaries, a field is represented by a pair of Hertz vectors — one electric, one magnetic — and the pair is enough to generate every electric and magnetic component. Stratton then makes the historical connection explicit in the chapter on spherical waves: Mie and Debye, in their classic treatments of scattering by a sphere, both made use of a pair of potential functions leading directly to the vector wave functions he is using, and Sommerfeld had pointed out how those connect to a radial Hertz vector.
Por qué importa aquíChapter 10 opens on Whittaker's result that the whole field can be rebuilt from two scalar potential functions, and says this is the ancestor of the Debye potentials and the Hertz vectors that working physicists use every day. Stratton is where to check it — a textbook that does exactly that, on real boundary-value problems, and that names the Mie and Debye pair of potentials in the same breath.
Qué afirma
01The integration of Maxwell's equations can be reduced to the determination of a vector and a scalar potential, which in homogeneous media satisfy one and the same differential equation — the starting point from which the whole potential-first practice follows.Section 1.11, ‘The Hertz Vectors, or Polarization Potentials’, opening paragraph, page 28
Settled physics02It was shown by Hertz that under ordinary conditions an electromagnetic field can be defined in terms of a single vector function — the Hertz vector, also called the polarization potential — with the vector potential taken proportional to its time derivative and the scalar potential fixed as minus its divergence.Section 1.11, pages 28 to 29, Eqs. 41 to 45; the footnote credits Hertz 1888 and the general solution to Righi, 1901
Settled physics03For bounded problems the representation uses a pair of Hertz vectors rather than one: Stratton states that under the specified conditions an electromagnetic field can be represented in terms of two Hertz vectors, and gives the two equations that generate the electric and magnetic vectors from them.Chapter VII, the two-Hertz-vector representation, Eq. 14, page 394
Settled physics04The same construction is what Mie and Debye used. Stratton's footnote records that the first thorough investigations of the electromagnetic problem of the sphere were made by Mie in 1908 and Debye in 1909, that both writers made use of a pair of potential functions leading directly to the vector wave functions in use here, and that Sommerfeld pointed out the connection between those solutions and a radial Hertzian vector.Section 7.11, footnote to Eq. 10, page 415
Settled physics05The technique is general working practice rather than a special trick: Stratton builds cylindrical fields from a Hertz vector directed along the axis, derives the retarded Hertz vector for radiation from a source distribution, and uses the same representation for dipole and quadrupole radiation and for propagation over a conducting plane.Section 6.1, ‘Representation by Hertz Vectors’, page 349; Section 8.3, ‘Retarded Hertz Vector’, page 430; Section 8.4 and the ground-wave sections of Chapter IX
Settled physics
La puerta de entrada
https://archive.org/details/electromagnetict031016mbpSOURCE READ. The full text of the 1941 first edition is openly readable in the Universal Library collection at the Internet Archive, identifier electromagnetict031016mbp, and the sections cited below were read there on 2026-09-11. No licence statement of any kind accompanies that scan, and a 1941 commercial monograph should be treated as in copyright, so this sheet carries a summary and short quotations and sends the reader to the scan. SCAN QUALITY. The optical character recognition of the Universal Library copy renders the equations unreliably — subscripts, script capitals and the Greek Pi used for the Hertz vector are frequently mangled. The prose is clean and is what the claims below rest on; the equation numbers are given so a reader can find the mathematics on the page rather than trust the transcription.
Cómo citarlo
Julius Adams Stratton (1941) Electromagnetic Theory. https://archive.org/details/electromagnetict031016mbp
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