From Current Literature

Inertia of Electric Charge Carriers in Copper and Aluminum

The use of inertia to prove the electronic nature of the carriers of electricity in metals was, as is known, first carried out by Tolman and Stewart[^1]. Kettering and Scott[^2] performed another experiment, also based on the inertia of electrons, but one that is, as it were, the inverse of the Tolman and Stewart experiment. In the latter, the appearance of an electromotive force was observed when a rotating coil was braked, whereas in the experiment of Kettering and Scott a change in the angular momentum of a suspended coil was observed when the current in it was changed. The experiment was carried out using all the resources of modern technique and was used for an accurate determination of \(m/e\) for the current carriers in metals. The result obtained by the authors differs from the accepted value of \(m/e\) (according to Bearden) by only \(0.2\%\).

The idea of the experiment is extremely simple. A coil of wire (three copper coils of different size and shape and one aluminum coil were used) was suspended as a torsion pendulum. When the current in the coil was switched, owing to the inertia of the electrons, the amplitude of oscillation changed. By measuring the magnitude of this change, it was possible to determine \(m/e\) on the basis of the following simple considerations.

An electron moving in a wire turn of mean radius \(r\) with mean angular frequency \(\omega\) possesses angular momentum \(Z = mr^{2}\omega\). The number of revolutions of the electron per second will be \(\omega/2\pi\), and the current carried by it is \(e\omega/2\pi = i\). Hence \(\omega = 2\pi i/e\), and \(Z = 2\pi r^{2} i\, m/e\). If the coil has \(N\) such turns and their mean cross-sectional area is \(A\), then \(Z = 2AiN\,m/e\). When the current in the coil is changed by an amount \(\Delta i\), the angular momentum changes by \(\Delta Z = 2A\Delta iN\,m/e\). It can be shown that if this change in angular momentum ...

...occurs when the pendulum passes through the center of oscillation, then the change in amplitude caused by it will be \(\Delta\theta=\Delta Z\frac{P}{2\pi I}\), where \(P\) is the period of the coil, and \(I\) is its angular momentum. Substituting the expression for \(\Delta Z\), we obtain

\[ \Delta\theta=\frac{\Delta i\,ANP}{\pi I}\cdot\frac{m}{e}. \]

In fact, the change of current was carried out by reversing its direction, so that \(\Delta i=2i\); what was observed was not the change of amplitude \(\Delta\theta\) itself, but, conventionally speaking, the displacement \(d\) of the spot of light reflected from the mirror connected with the coil, when it was turned through twice the amplitude, on a scale at a distance \(a\) from the mirror, so that \(\Delta\theta=\frac{d}{2a}\). The final formula, therefore, has the form:

\[ d=\frac{4ANiP\cdot a}{\pi I}\cdot\frac{m}{e}. \]

In view of the smallness of the effect and the need to protect the apparatus from disturbances considerably exceeding the effect, the experiment is very difficult. Nevertheless, it was carried out so carefully and under such good conditions that the results proved to be very stable. The apparatus was installed at a special station built by the research laboratories of General Motors for observations requiring the fullest possible elimination of vibrations and magnetic disturbances. The station is located approximately 1000 feet from the nearest road and is almost completely free from all artificial oscillations and magnetic disturbances. It consists of a small building and a basement for installing the sensitive apparatus. The observer takes readings while located in the upper room, with the aid of a special remote-control system.

The authors characterize the basement as an ideal room for precise measurements. There are no air currents in it, it is absolutely dark, and the temperature change in it over 24 hours does not exceed \(1.4^\circ\)F. In the basement there are three mutually perpendicular systems of coils with a common center. These coils were used to neutralize and control the various components of the earth’s magnetic field. A special device, located in the upper room and consisting of a magnetic needle suspended inside a solenoid and carrying a mirror, an optical illumination system, and controlling photoelectric cells, automatically compensated the variations of the west-east component of the earth’s field, which alone created difficulties in these experiments.

The arrangement of the apparatus is shown in Fig. 1. Here \(J\) is the coil, \(F\) the mirror, by means of which the deflections of the torsion pendulum were recorded. These negligibly small deflections were amplified by...

Fig. 1.

Labels in the figure: A, B, C, D, E, F, G, H, I, J, K, L.
Scale: 3″.

Mirror capillaries

Photocell  Prism  Photocell

Slit

Lamp

Fig. 2.

by means of an optical system constructed according to the type of so-called optical deflection amplifiers. The arrangement used by the authors is distinctive and deserves description, since it can be used successfully for readings of small galvanometer deflections. Light from a 6-volt incandescent lamp (Fig. 2), with the aid of a powerful condenser, was concentrated on the slit. The lamp was supplied by eight storage batteries connected in parallel, which gave a very constant voltage over long intervals of time. By means of another system of lenses, the image of the slit, through

Fig. 3.

the mirror of the coil, was projected onto a dividing prism, which divided the light into two parts and sent the beams to two photoelements (vacuum photoelements with an external photoeffect were used). The currents of these photoelements were sent directly (i.e., without tube amplification) into a system of two galvanometers, the connection diagram of which is shown in Fig. 3. Obviously, the short-period galvanometer located at the center of the circuit measures the difference of the photocurrents, i.e., gives readings proportional to the rotation of the coil mirror, while the second galvanometer reads the sum of the photocurrents, i.e., a quantity proportional to the total amount of light incident on the photoelements.

on the photocells. The galvanometers were located at a distance of 5 meters from the photographic recording device.

The amplification provided by the system described was equivalent to reading the deflection of the mirror on a scale several thousand meters away. In determining \(\frac{m}{e}\), the amplification was adjusted so that it was equivalent to a reading on a scale 1000 meters away.

The paper further gives a detailed description of the method of suspending and mounting the coil, the measurement procedure, systematic errors, and ways of eliminating them. The results obtained by the authors may be summarized in the following table:

Average for all coils . . . . . \(5.69 \cdot 10^{-9}\) g/coul

Accepted value of \(\frac{m}{e}\) for electrons (according to Bärdž) . . . . . \(5.68 \cdot 10^{-9}\) g/coul

The authors emphasize—and consideration of their figures confirms this—that, owing to the perfection of the experimental arrangement, the results are characterized by great stability.

The experiment of Kettering and Scott is of great interest not only from the standpoint of experimental technique. It should be regarded as the most direct and accurate determination of the mass (inertia) of electrons, and as proof, corresponding to the contemporary level of technique, of the identity of the carriers of electric current in different conductors.

E. Shpolsky

CITED LITERATURE

1. R. C. Tolman and T. D. Stewart, Phys. Rev., 8, 97, 1916; R. C. Tolman, S. Karrer and E. W. Guernsey, Phys. Rev., 21, 525 (1933); R. C. Tolman and L. M. Mott-Smith, Phys. Rev., 28, 794 (1926). For a brief description, see, for example, Becker, Electron Theory.
2. C. F. Kettering and G. G. Scott, Phys. Rev., 66, 257 (1944).