ELECTRICAL AND MAGNETIC SPECTROSCOPY.

V. K. Arkadiev.

An electromagnetic wave, passing through some body, usually has in it a different velocity than in empty space and often propagates in the body while gradually losing its energy along the way, i.e., undergoing absorption. The velocity of very long waves in dielectrics is determined by their dielectric coefficient \(\varepsilon_{\infty}\), which can be determined electrostatically from the increase in the capacitance of a capacitor, and by the magnetic permeability \(\mu_{\infty}\), which can be measured with a magnetometer. If the electromagnetic wave is very short, then its electric and magnetic fields change so rapidly that the electric and magnetic particles do not have time to be displaced, and in the substance no electric or magnetic polarization has time to arise that would influence the velocity of the wave; then there is no friction that causes the strong absorption of waves of medium length. Therefore the absorption of short waves is very small and their velocity in a substance does not differ from the velocity in empty space; such are X-rays, whose absorption is negligible—all bodies are transparent to X-rays, their velocity in a substance is equal to the velocity in empty space, and the refractive index of X-rays is equal to 1. This occurs because, in the high-frequency electric fields of X-ray waves, electrons and ions do not have time to be displaced appreciably. The oscillations of X-rays lie on the far side of the crisis of the electrical properties of matter, in the region where the dielectric coefficient is equal to 1.

In the middle part of the spectrum, where the number of oscillations of the electromagnetic wave coincides with or is close to the number of oscillations of the electrical centers, we have a region of abrupt changes in the refractive index and in the dielectric coefficient \(\varepsilon\)—the region of electrical dispersion and the region of strong absorption of rays, the region of electrical absorption. Here in dielectrics there appears the so-called conductivity of polarization, denoted by \(\sigma\). The appearance of this factor of electrical conductivity of an insulator is a very peculiar phenomenon: at a definite frequency of oscillation, precisely when the centers embedded in the substance are most strongly set into oscillation (resonate) under the action of the alternating field of the wave,

in the diagram. There too are indicated the proper wavelengths \(\lambda_0\) of the elementary magnets lying in this region and their friction \(\theta\).

In the region of this absorption band the magnetic permeability is variable. In one case it is even less than 1 and is equal to 0.80.

By analogy with dielectrics, we must conclude that in this region of periods magnetic bodies must also exhibit magnetic conductivity. This paradoxical fact leads to a number of consequences which make it possible to speak of ferromagnetic bodies in the same way as we are accustomed to speaking of conductors of electricity.

Namely, upon magnetization reversal in an alternating field, even if hysteresis does not exist, we must have a certain loss of energy and the production of heat, caused by the viscous friction of the elementary magnets. This leads to a law for the development, in \(1\ \mathrm{cm}^3\) of a magnetic body, of \(W_m\), analogous to Joule’s law, namely

\[ W_m = \rho H^2 t, \]

which coincides with the electrical Joule law \(^{1}\)

\[ W_e = \sigma E^2 t. \]

The magnetic conductivity \(\rho\) in centimeter hertzian waves proves to be of the order of \(10^{10} — 10^{11}\) units. To estimate this number, let us imagine that already in a constant magnetic field iron exhibits the same magnetic conductivity. It is clear that in such a case any transformer with a closed magnetic circuit could be supplied with direct current, and it would give a constant transformed electric current \(^{2}\). The cross-section of its iron, owing to the great magnetic conductivity of the magnetic core (\(\rho = 10^{11}\) CGSM), could be made quite negligible, and the whole iron circuit could be realized in the form of a single turn of thin iron wire. However, this is limited by the magnetic Joule law written above, from which it follows that one turn of thin wire would not withstand such a load and would quickly burn out as a result of the enormous magnetic friction.

Assuming that the elementary magnets in a ferromagnetic metal rotate according to the same laws of elastic-viscous motion as are usually ascribed to the displacement of electric centers in dielectrics—

\(^{1}\) Here Joule’s law is written for \(1\ \mathrm{cm}^3\) of substance; indeed, the current strength in \(1\ \mathrm{cm}^3\) is \(i = \dfrac{e}{r} = \dfrac{E1}{r}\); the resistance of \(1\ \mathrm{cm}^3\) is \(r = \dfrac{1}{\sigma}\); hence \(W_e = i^2 r t = \sigma E^2 t\).

An analogous derivation also applies to the magnetic Joule law.

\(^{2}\) The current would be due to the constant electric field encircling the iron wire with a constant magnetic current.

case, one obtains for the permeability \(\mu\) and the magnetic conductivity \(\rho\) the following quantities:

\[ \tag{3} \mu=1+(\mu_\infty-1)\frac{1-\nu^2}{\theta^2\nu^2+(1-\nu^2)^2} \quad \text{and} \quad \rho=\frac{\mu_\infty-1}{2T_0}\, \frac{\theta\nu^2}{\theta^2\nu^2+(1-\nu^2)^2}. \]

The magnitude of the refractive coefficient and of the absorption is determined from the expressions\(^1\):

\[ \tag{4} \begin{aligned} 2n^2&=\sigma'\left(\sqrt{\mu^2+\rho'^2}-\rho'\right)=\sigma'\mu_n,\\ 2k^2&=\sigma'\left(\sqrt{\mu^2+\rho'^2}+\rho'\right)=\sigma'\mu_k, \end{aligned} \]

where \(\rho'=2\rho T\).

The absorption coefficient \(k\), which determines the decrease of the wave amplitude with distance \(x\) by the formula \(e^{-kx}\), is

\[ \frac{2\pi k}{\lambda}=2\pi\sqrt{\frac{\sigma}{c}}\sqrt{\frac{\mu_k}{\lambda}}. \]

The coefficient presented in Fig. 2 is \(S=\sqrt{\frac{\mu_k}{\lambda}}\). The lines show the theoretical course of the quantities \(\mu_k\) and \(\mu_n\). The light circles represent measurements, from the absorption of waves in ferromagnetic wires, of the quantity \(\mu_k\). The agreement of the theoretical quantities with the experimental ones is entirely satisfactory.

From the formulas (2) and (4) given above we see that \(n\) and \(k\), in the case of electrical and magnetic dispersion, are expressed by means of two terms

\[ \begin{aligned} \sigma_n'&=r+a, & \sigma_k'&=r-a,\\ \mu_k&=r+\beta', & \mu_n&=r-\beta', \end{aligned} \]

where \(a\) replaces \(\varepsilon\) and \(\mu\), \(\beta'\)—\(\sigma'\) and \(\rho'\), and \(r=\sqrt{a^2+\beta'^2}\). The study of the course of the quantities \(r\pm a\) constitutes the subject of the theory of electrical dispersion and absorption, in particular of ordinary optical dispersion; the study of the quantities \(r\pm\beta'\) is the subject of the theory of magnetic dispersion and absorption.

Recently the two terms \(\mu_k\) and \(\mu_n\) have also found application in electrical engineering, where, with their aid, those electromagnetic processes become amenable to theoretical investigation in which the absorption of energy in iron is caused not only by viscous friction in the rotation of elementary magnets, but also by other causes, such as hysteresis and Foucault currents (Uller, Tonks, Truksa, Gans).

The study of the course, as a function of wavelength, of the quantities

\[ \mu=\sqrt{\mu_n\mu_k},\quad 2\rho'=\mu_k-\mu_n \]

and of \(\mu_k\) and \(\mu_n\) themselves for various ferromagnetic metal-

\(^1\) The general expressions for \(n\) and \(k\) are:

\[ 2n^2=\sqrt{(\varepsilon^2+\sigma'^2)(\mu^2+\rho'^2)}+\varepsilon\mu-\sigma'\rho' \quad \text{and} \quad 2k^2=\sqrt{(\varepsilon^2+\sigma'^2)(\mu^2+\rho'^2)}-\varepsilon\mu+\sigma'\rho'. \]

From them (2) and (4) are obtained as special cases.
See V. Arkad’ev, Zh. R. F. O. 45, 312, 1913.

…of metals and their compounds, i.e., passive magnetic spectra, constitutes the subject of passive magnetic spectroscopy. Its difference from the old passive electric spectroscopy, un—

Fig. 2. Bands of magnetic absorption \(S=\sqrt{\dfrac{\mu_k}{\lambda}}\) in iron and nickel wires, and their apparent permeability \(\mu_k\) and \(\mu_n\).

the further behavior of the refractive index, absorption, reflection coefficient, etc., consists in the fact that the former investigates the effect on matter of the electric vector of the electromagnetic wave, and the latter—that of the magnetic vector of the same wave. We see that both these branches of general electromagnetic spectroscopy are entirely equivalent.

If the old spectroscopy has revealed to us many properties of bodies and has clarified that broad spectral region of the natural oscillations of the particles of matter which extends from the boundary of the ultraviolet rays and penetrates into the region of Hertzian rays, then no less valuable results may rightly be expected from magnetic spectroscopy, since precisely the magnetic properties of matter, and especially the magneton, at the present time present much that is obscure and enigmatic. Sommerfeld says in his well-known book on the structure of the atom: “The day will come when instructive results of investigations on magnetism will enable us to decipher Bohr’s magneton, or, what is the same thing, Planck’s quanta, and will make it possible to draw with complete clarity the picture of the quantum structure of matter.”

Fig. 3. \(R\)—resonance of electric or magnetic centers; \(\delta_p\)—lag of their phase and of the polarization phase behind the phase of the field; \(\delta_c\)—lag of the phase of induction; \(r\)—the value \(\sqrt{\alpha^2+\beta^2}\); the refractive index \(n\) in dielectrics is determined from the equation \(2n^2=r+\alpha\), the absorption coefficient in them from the equation \(2k^2=r-\alpha\); the apparent permeability
\[ \mu_k=r+\beta',\qquad \mu_n=r-\beta'. \]

LITERATURE

(principal works).

1. W. Arkadiew. Ueber die Reflexion elektromagnetischer Wellen an Drähten. Ann. der Phys. 45, 133, 1914. Ж. Р. Ф. О. 45, 46, 1913.

2. R. Gans. Bemerkung zu meiner Arbeit „Das Verhalten Hertz’scher Gitter“. Ann. d. Phys. 66, 427, 1921.

3. W. Arkadiew. Ueber die Absorption elektromagnetischer Wellen an zwei parallelen Drähten. Ann. d. Phys. 58, 105, 1919. Ж. Р. Ф. О. 44, 1912.

1. V. Arkadiev. Ferromagnetic properties as a function of wavelength. Zh. R. F. O. 45, 312, 1913.

2. W. Arkadiew. Das Verschwinden der ferromagnetischen Eigenschaften bei den kürzesten elektrischen Wellen. Phys. Zs. 14, 561, 1913.

3. W. Arkadiew. Eine Theorie der elektromagnetischen Feldes in ferromagnetischen Metallen. Phys. Zs. 14, 928, 1913. Zh. R. F. O.

4. V. Arkadiev. Theory of the magnetization of a body in constant and alternating fields and its application to practical problems of electrical engineering. Telegraphy and Telephony without Wires, issue 7, 1920, p. 135.

5. V. Arkadiev. Contemporary problems in the study of the magnetization of a body and substance in constant and alternating fields. “Physics”—Journal of the Moscow Physical Society named after Lebedev, p. 320, 1922.

6. Richard Gans und Ramon G. Loyarte. Die Permeabilität des Nickels für schnelle elektrische Schwingungen. Ann. d. Phys. 64, 209, 1921.

7. Richard Gans. Die Permeabilität des Nickels für kurze Hertz’sche Wellen und die Messungen von Arkadiew. Ann. d. Phys. 64, 250, 1921.

8. W. Arkadiew. Die Theorie des elektromagnetischen Feldes in ferromagnetischen Metallen und die Berechnungen von R. Gans. Ann. d. Phys. 65, 643, 1921.

9. R. Gans. Bemerkungen zu der Arbeit „Die Permeabilität des Nickels für schnelle elektrische Schwingungen von Richard Gans und Ramon G. Loyarte und die Priorität Arkadiew. Ann. d. Phys. 66, 429, 1921.

10. W. Arkadiew. Erklärungen zu der Arbeit von R. Gans „Magnetische Permeabilität des Nickels für schnelle elektrische Schwingungen und die Messungen von Arkadiew“. Ann. d. Phys. 66, 130, 1921.

11. B. A. Vvedensky. On the rate of demagnetization of iron. Scientific Proceedings of the State Publishing House, p. 320, 1922.

12. B. Wwedensky. Ueber die Wirbelströme bei spontaner Aenderung der Magnetisierung. Ann. der Phys. 64, 609, 1921.

13. B. Wwedensky. Magnetische Viskosität in sehr dünnen Eisendrähten. Ann. der Phys. 65, S. 110, 1921.

14. W. Kartschagin. Ueber die selektive Absorption elektrischer Wellen an Eisendrähten und über die magnetische Permeabilität des Eisens. Ann. d. Phys. 67, 325, 1922.

15. Vvedensky and K. Theodorchik. On the initial permeability of iron in radio-frequency fields. Telegraphy and Telephony without Wires, No. 13, p. 248, 1922.

16. B. Wwedensky und K. Theodortschik. Ueber die Abhängigkeit der Permeabilität der Eisendrähte von Frequenz im Wellenlängenbereich von 54 bis 705 m. Ann. d. Phys. 68, 463, 1922.

17. W. Arkadiew. Das Spektrum der magnetischen Permeabilität in dem Bereiche der Wellenlängen zwischen 1 cm. und 1 km. Phys. Zs. 22, 511, 1921.

18. V. Arkadiev. On the process of excitation by a spark of rapid electrical oscillations and on the absolute measurement of their amplitude. “Physics.”

19. V. Arkadiev. Dependence of the permeability of iron and nickel on the strength and period of an alternating magnetic field of very slow and very rapid electrical oscillations. “Physics.”

20. V. Arkadiev. New paths in the study of the molecular world. “Science and Technology,” No. 2–3, p. 20, 1922. Separate publication: “The Molecular World and Its Study.” Moscow, 1924.

21. L. Page. Magnetisation in Weak Fields as a Function of Frequency. Phys. Rev., 21, 456, 1923.

22. V. Arkadiev. Magnetic Spectroscopy. Published by the Scientific-Technical Department of the Supreme Council of National Economy. Issue 4. Moscow, 1924.