Potential Distribution in a Liquid Dielectric Layer
Abstract Generated abstract
This paper investigates how electric potential is distributed between capacitor plates separated by liquid dielectrics, with particular attention to time-dependent conductivity, residual charge, and possible ionic accumulation near electrodes. Using an ionic-conduction analogy with gases, the author argues that nonuniform potential gradients should arise under saturation current, then tests this with specially constructed condensers, movable or fixed needle probes, electroscopes, and electrometers in liquids including castor oil, toluene, turpentine, petroleum, and liquid vaseline. The experiments find nearly linear potential distribution in castor oil, whose conductivity was observed not to vary with time, but curved distributions in other dielectrics, with curvature increasing at higher voltages and large potential drops near electrodes. The results are presented as supporting the applicability of ionic theories of gaseous conduction to liquid dielectrics, with tentative evidence that negative ions may be more mobile than positive ions.
Full Text
V. D. Kuznetsov.
Potential Distribution in a Layer of Liquid Dielectric
If a constant potential difference is applied to the plates of some capacitor filled with a liquid dielectric, then for certain dielectrics a decrease in the current strength with the passage of time is observed; this occurs rapidly at first, and then slowly. Furthermore, if, after some time from the moment when the potential difference was applied, the electric field is removed, then for certain dielectrics the so-called phenomenon of residual charge is observed.
Assuming that there is an analogy between the processes of the passage of electricity through liquid dielectrics and through ionized gases, and that the electric current through liquid dielectrics is due to the existence of positive and negative ions, we arrive at the conclusion that ions may gradually accumulate near the electrodes: positive ones at the cathode and negative ones at the anode.
In other words, we may introduce the concept of volume density and regard it as positive in that place where the number of positive ions is greater than that of negative ones, and negative in the place where negative ions predominate. The appearance of a positive density at the cathode and a negative one at the anode creates a reverse electric field, weakening the current strength due to the external potential difference. After the electric field is removed, the grouped ions, repelling one another, will tend toward a uniform distribution and by their motion will create a return electric current, opposite to the direct current.
The correctness of the views expressed may be tested by studying the distribution of potential in a layer of liquid dielectric between the plates of a capacitor to which an electromotive force has been applied.
First we shall consider several possible cases of potential distribution.
1) The volume density throughout the dielectric during the passage of current is equal to zero. This case may occur when the recombination of ions is large, as in aqueous solutions of salts, and when the electromotive force of polarization is equal to zero. During the flow of electric current an ion moves in the dielectric as though jumping from one ion of opposite sign to another, until from the last ion it passes directly to the electrode. Despite the motion of electricity and the existence of an electric field, the volume density is everywhere equal to zero, and the potential distribution is represented by the straight line \(AB\) (Fig. 1). The field intensity throughout the whole column will be the same and equal to
\[ X = \frac{V}{d} = \operatorname{tg}\varphi, \]
where \(V\) is the potential difference, \(d\) the distance between the electrodes, and \(\varphi\) the angle of inclination of the straight line \(AB\) to the axis of abscissas, along which is laid off the distance from the point under study to one of the electrodes.
2) If at the positive electrode \(A\) there is an excess of negative ions, and at the negative electrode \(B\) an excess of positive ions, then the potential distribution will be represented by the curve \(AA_{1}B_{1}B\). In this case the field intensity, or the potential gradient, will be greater at the electrodes than in the middle.
3) If, conversely, there is a positive volume density at the anode, and a negative one at the cathode, then the curve will be \(A A_2 B_2 B\). The field in the middle is more intense than at the electrodes.
4) If the mobility of ions of one sign is greater than the mobility of ions of the other sign, then the curves \(A A_1 B_1 B\) and \(A A_2 B_2 B\) will not be symmetrical, and their points of inflection will be shifted in the direction of motion of the faster ions.
5) Suppose that the current has been flowing for some time and the potential distribution is represented by the curve \(A A_1 B_1 B\) (Fig. 1). If the plates of the condenser are briefly connected, then the potential distribution will be represented by the curve of Figure 2, i.e., near the anode \(A\) there will be a negative potential, and near the cathode \(B\) a positive potential.
The ionic theory of electrical conductivity leads to the necessity of a nonuniform distribution of potential, especially under saturation current.
Indeed, the saturation-current density \(J\) is expressed by
\[ J = \varepsilon q d, \]
where \(q\) is the number of ions formed in \(1\) sec. in \(1\ \mathrm{cm}^3\), \(\varepsilon\) is the elementary charge, and \(d\) is the distance between the electrodes. But this same current density \(J\) can be expressed otherwise:
\[ J = \varepsilon X (n_1 k_1 + n_2 k_2), \]
where \(X\) is the electric-field strength, \(n_1\) and \(n_2\) are the numbers of positive and negative ions in \(1\ \mathrm{cm}^3\), and \(k_1\) and \(k_2\) are their mobilities.
If, under saturation current, the field strength \(X\) were the same throughout the entire column, equal to
\[ X = \frac{V}{d}, \]
where \(V\) is the difference of potentials applied to the plates of the condenser, then we would have
\[ J = \varepsilon \frac{V}{d} (n_1 k_1 + n_2 k_2), \]
i.e., the saturation-current density would depend on the potential difference \(V\), which contradicts the very definition of the concept of saturation current. Consequently, under saturation current we must necessarily regard the potential distribution as nonuniform, and the more nonuniform the higher \(V\) is, i.e., the greater the deviation from Ohm’s law. At different points along the column of dielectric the field strength \(X\) is different and is a function of the distance \(x\) of the point from one of the electrodes,
\[ X = X(x). \]
The potential difference \(V\) is expressed by the definite integral
\[ V = \int_{x=0}^{x=d} X(x)\,dx, \]
extended over the entire distance \(d\) between the electrodes.
In the dielectric there may be such points at which \(X\) differs little from zero, and such points where \(X\) is considerably greater than \(\frac{V}{d}\).
Further, in the stationary state the current density \(J\) must be everywhere the same, since otherwise at some points there would be a continuous accumulation of electricity; and this entails that the concentrations of ions \(n_1\) and \(n_2\) must be different in different places. The numbers \(n_1\) and \(n_2\) must be the same where the field strength \(X\) is equal to zero, and different in places where the potential gradient is not equal to...
is zero, while the difference between \(h_1\) and \(h_2\) reaches a maximum at the points of greatest field strength.
From the theoretical point of view, an experimental investigation of the distribution of potential in a dielectric at high voltages, when the current becomes saturated, is of great interest.
Despite the importance of the question under consideration, very little has been done in this area. I know of only one work in which, among other things, the distribution of potential in a layer of liquid dielectric was studied.
E. v. Schweidler1 made observations on the distribution of potential in toluene. His measuring condenser consisted of two vertical zinc plates \((9 \times 6\ \mathrm{cm})\), placed 23 mm apart. One plate was connected to earth through a galvanometer, while the other had a potential of \(+300\) volts. Between the electrodes there was placed a probe (a platinum wire) connected to an Exner electroscope, which made it possible to determine the potential with an accuracy to \(\pm 1\) volt. The distance from the probe to the electrodes was determined with an accuracy to \(0.1\) mm.
On the basis of his observations Schweidler concluded that the field strength is more intense near the electrodes than in the middle, and that a negative free charge appears at the anode and a positive one at the cathode. The author gives only two series of observations at one and the same potential difference; moreover, the numbers do not agree with one another, and therefore the conclusion concerning the accumulation of charges near the electrodes seems to me little convincing.
To study the distribution of potential in a layer of liquid dielectric, I constructed a special condenser, shown in Fig. 3. A glass vessel, cubic in shape with a side of 7 cm, was provided with an ebonite lid \(EK\), which had a groove along which three ebonite sliders, marked in the figure by the numbers 1, 2, and 3, could move. Brass wires 2 mm thick passed through the sliders; to two of the wires were soldered square plates \((30 \times 30\ \mathrm{mm})\), \(A\) and \(B\), made of tinned sheet iron; in the third wire a recess was drilled, into which an ordinary thin sewing needle was soldered in such a way that its point was opposite the centers of the plates \(A\) and \(B\). Next to the groove on the ebonite plate a millimetre scale, made by means of a dividing machine, was applied, serving to determine the position of the electrodes and the probe.
Preliminary experiments showed that the needle rather quickly (from several seconds to several minutes—depending on the dielectric) acquired the potential of the given point. The use of a Wollaston wire as a probe proved irrational, since the results obtained were indefinite. Likewise, a probe made of a bent sewing needle proved unsuitable, since it gave different readings depending on the direction in which the bend of the needle went. This appeared quite understandable if one takes into account that, in a plane condenser, where the potential at all points of a plane vertical and parallel to the electrodes has approximately one and the same value, all points of a straight vertical needle coincide with an equipotential surface, whereas a curved needle intersects different level surfaces.
The arrangement of the apparatus is shown in Fig. 4. The plate \(A\) of the measuring condenser \(IK\) described above was connected through switch \(\mathrm{P}_1\) with one of the poles of a battery \(B_1\) of small accumulators,
the other pole, which was led to ground; the second plate, \(B\), was always connected to ground. Probe \(3\) was connected to the leaf of Wilson’s electroscope, \(EV\), the plate \(P\) of which was charged through switch \(P_2\) from a battery \(B_2\) of small accumulators. Key \(K\) served for grounding the probe and the leaf of the electroscope.
First of all, tests were made with various probes; the tests led to the conclusion that a thin sewing needle with a good point, examined under a microscope, is a quite reliable collector. This was evident from the fact that, after the probe was insulated, the leaf of the electroscope rather quickly came to rest and remained in one and the same position for as long as desired. When any charged body, for example a hand, was brought near the electroscope, the leaf received a deflection in one direction or another, but soon assumed its former position. This latter circumstance made it unnecessary to protect the connecting wires from external electrical influences, as is almost always required when studying the electrical conductivity of liquid dielectrics.
In each investigation a suitable sensitivity of the electroscope was established. It was not great, and the deflection of the leaf was linearly dependent on its potential. The sensitivity was changed by moving plate \(P\). The base of the electroscope was set horizontally by means of a leveling screw and a level. For charging plate \(P\) there was used a battery of small accumulators with a potential difference of about 55 volts. The graph in Fig. 5, as an example, shows the results of one of the calibrations of the electroscope, when its sensitivity had the greatest of the values used.
The first investigations of the potential distribution were carried out with castor oil, which was chosen because previous experiments had established the complete independence of the electrical conductivity of this dielectric from time. On this basis one could expect that the potential gradient at all points of this dielectric would have the same value. In these experiments the measuring condenser had a somewhat different construction from that shown in Fig. 3. Instead of an ebonite cover there was a paraffin plate, in which, at a distance \(D = 34\) mm, plates \((30 \times 30\ \mathrm{mm})\) of tinned sheet iron were fastened on copper wires. In addition, several holes were made in the plate, into which the probe was placed. The distance between the electrodes and the point of the probe was measured with an accuracy of up to \(0.5\) mm by means of a mirror scale placed outside the cuvette. The results are given in Table I and shown graphically in Fig. 6.
Table I. Castor oil. \(V = +55\) volts, \(D = 34\) mm. 25. 1. 19.
| 3 | 14 | 24 | 22 | 25 | 29 | 3 | |
|---|---|---|---|---|---|---|---|
| \(d\) | 3 | 14 | 24 | 22 | 25 | 29 | 3 |
| \(a\) | 33.3 | 47.0 | 60.0 | 58.0 | 63.0 | 66.0 | 33.0 |
| \(a_0\) | 29.0 | 29.0 | 29.0 | 29.0 | 29.0 | 29.0 | 29.0 |
| \(a-a_0\) | 4.3 | 18.0 | 31.0 | 29.0 | 34.0 | 37.0 | 4.0 |
| \(V\), volts | 6 | 22 | 39 | 36 | 41 | 47 | 5 |
In the first row of Table I are placed the values of the distance \(d\), in mm, from the point of the probe to electrode \(B\), connected to ground; in the second, the positions \(a\) of the electroscope leaf on the microscope scale when the leaf and probe are insulated; in the third, the positions \(a_0\) of the leaf when it is connected to ground; and in the fourth, the differences between the first and second positions, i.e. the deflections of the leaf under the influence of the given poten-
did. In the last line are given the values of the probe potential according to the calibration.
The potential difference \(V\) on the plates of the condenser was 55 volts, with plate \(A\) connected to the positive pole of the battery \((V=+55\ \text{volts})\). The observations consisted in first reading on the microscope scale the position \(a_0\) of the leaf connected to earth; then the leaf was insulated and, when the deflection ceased to increase, a second reading \(a\) was made.
All subsequent investigations were carried out with the measuring condenser shown in Fig. 3. As dielectrics there were used: purified and several-times distilled toluene, technical turpentine (terebenum), and purified petroleum (rectificat). The results of the observations are given partly in Tables II and III and are represented graphically in Figs. 7, 8, 9, 10, and 11. The meanings of the letters in the tables are the same as in Table I.
Table II. Toluene. \(V=\pm 300\) V; \(D=18\) mm. \(27^\circ \pm 1^\circ\).
| \(V\) | Quantity | 18 | 16 | 14 | 12 | 10 | 8 | 6 | 4 | — |
|---|---|---|---|---|---|---|---|---|---|---|
| \(V=+300\) V | \(d\) | 18 | 16 | 14 | 12 | 10 | 8 | 6 | 4 | — |
| \(V=+300\) V | \(a\) | 93.0 | 57.0 | 35.0 | 25.0 | 18.0 | 12.5 | 7.0 | 4.5 | — |
| \(V=+300\) V | \(a_0\) | 0.0 | » | » | » | » | » | » | » | — |
| \(V=+300\) V | \(a-a_0\) | 93.0 | 57.0 | 35.0 | 25.0 | 18.0 | 12.5 | 7.0 | 4.5 | — |
| \(V=-300\) V | \(d\) | 18 | 16 | 14 | 12 | 10 | 8 | 6 | 4 | 2 |
| \(V=-300\) V | \(a\) | 90.0 | 54.0 | 35.0 | 25.0 | 17.7 | 11.5 | 6.7 | 4.0 | 1.8 |
| \(V=-300\) V | \(a_0\) | 0.0 | » | » | » | » | » | » | » | » |
| \(V=-300\) V | \(a-a_0\) | 90.0 | 54.0 | 35.0 | 25.0 | 17.7 | 11.5 | 6.7 | 4.0 | 1.8 |
Table III. Terebenum. \(V=+220\) V; \(D=30\) mm. 1·2·19.
| 2 | 5 | 10 | 15 | 20 | 25 | 30 | 25 | 20 | 15 | 10 | 5 | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a-a_0\) | 10.6 | 13.5 | 19.6 | 30.0 | 40.5 | 57.0 | 72.5 | 63.5 | 46.2 | 31.5 | 21.2 | 13.5 | 9.0 |
| \(a_0\) | 7.5 | 7.5 | 7.3 | » | » | » | 7.0 | » | » | » | » | » | » |
| \(a\) | 3.1 | 6.0 | 12.3 | 22.7 | 33.2 | 49.7 | 65.5 | 56.5 | 39.3 | 24.5 | 14.2 | 6.5 | 2.0 |
From the results obtained the following conclusions may be drawn:
1) A sewing needle is a sufficiently reliable probe. This is evident from the fact that the curves \(a-a_0=f(d)\), for increasing and decreasing \(d\), coincide with one another within the limits of the errors of observation (Fig. 7);
2) All the curves \(a-a_0=f(d)\) have their convexity toward the axis of abscissae, along which the values of the distance \(d\) are laid off. This means that, as the probe approaches the charged electrode, the potential increases more rapidly than the distance \(d\) decreases, i.e. the electric field in the liquid dielectric is not homogeneous.
3) With an increase of the potential difference \(V\) between the plates, the curvature of the curve increases (Figs. 7 and 8).
4) With a change in the sign of the electric field, the form of the curves does not change (Figs. 8 and 10).
5) The nonuniform distribution of potential must be ascribed to the property of the dielectric, and is not a consequence of the construction of the condenser. This is clear from the fact that, for castor oil, with the same condenser, the field strength was everywhere the same.
6) The distribution of potential is linear for that dielectric whose electrical conductivity does not change with the passage of time (castor oil), and nonlinear for those dielectrics whose electrical conductivity
in which, at constant voltage, it decreases with time (toluene, turpentine, and petroleum).
As we have seen, the validity of the fundamental ideas of the ionic theory of the conductivity of liquid dielectrics can be tested by studying the fall of potential along a column of dielectric at high voltages, when deviations from Ohm’s law begin and the current approaches saturation.
The experiments described above, carried out at comparatively low voltages, while of interest in themselves, are nevertheless insufficient to confirm the theory.
In what follows I describe investigations of the distribution of potential at high voltages. These investigations lasted only 5 days and covered only an insignificant part of the planned program; however, the results obtained are so interesting that I permit myself to publish them as a preliminary communication.
Fig. 12 shows a diagram of the arrangement of the apparatus. From the conductors of the electrophoric machine, EM, of Wommelsdorf, wires led to switch \(P_1\), which connected one of the poles of the machine to ground and connected the other pole, by means of switch \(P_2\), through the sensitive mirror galvanometer \(G\), with electrode \(A\) of the measuring capacitor \(IK\), filled with the dielectric under investigation. This same pole of the electric machine was connected to the inner coatings of two large Leyden jars \(LB\) and to high-voltage electrometer \(E_1\), a Braun-type electrometer made by M. Kohl. The galvanometer could be shunted by means of the resistance box \(MS\). The multi-position switch \(MP\) consisted of a paraffin disk with 14 recesses around the circumference and one recess in the center. All the recesses were filled with mercury and could be connected by a metal arc to the central recess, which was connected to the high-voltage electrometer \(E_2\) made by Günther und Tegetmeyer, of the Braun electrometer type, calibrated at the Phys.-Techn. Reichsanstalt. Two of the mercury contacts of switch \(MP\) were connected to electrodes \(A\) and \(B\), and the remaining 12 to the probes of the measuring capacitor. Electrometer \(E_1\) served for observing the constancy of the potential of the machine, and electrometer \(E_2\) for determining the potentials of the electrodes and probes. The Leyden jars were included in order to reduce fluctuations in the potential difference and to facilitate maintaining its constancy. The sensitivity of the galvanometer “Granta 15” from Pave and Co., Cambridge, was \(7.85 \cdot 10^{-9}\) ampere per 1 mm of deflection at a distance from mirror to scale of 123 cm; its resistance was 288 ohms.
The measuring capacitor consisted of a glass hollow cube (inside dimension 50 mm) and two electrodes of tinned sheet iron (30 × 30 mm).
Between the electrodes were placed 12 ordinary sewing needles (No. 4), which passed through the paraffin cover of the vessel. The needle points ended on the straight line joining the centers of the electrodes. The needles proved to be sufficiently good probes, except for two (4 and 5); they assumed the potential of the given point comparatively quickly (within 1–2 minutes). Probe 4 proved rather unsatisfactory. It indicated a potential below the true one, and this discrepancy increased as the strength of the electric field increased. The point of this probe was blunter than the others. Probe 5 gave incorrect readings at high voltages. From experience I became convinced that the quality of a probe should be tested at high voltages (about \(2.5 \cdot 10^3\) volts/cm), since
at low voltages almost all the needles perceive the potential sufficiently well.
The distances between the points of the probes were measured with a movable microscope. Table IV contains the results of the measurements.
Table IV. 2·7·19.
| Probe or electrode | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Distance from A…. | 2·65 | 4·90 | 6·50 | 8·65 | 11·12 | 13·75 | 15·85 | 18·80 | 21·65 | 24·70 | 27·05 | 28·95 | 30·65 |
The observations of the potential distribution consisted in the following. The motor rotating the electric machine was set in motion; when the potential difference at the poles of the machine became constant, electrometer \(E_2\) was connected in turn with the electrodes and probes, and its readings were observed, each time before connection with a probe or with an electrode the electrometer being discharged to earth. In addition, the time was noted by the clock and the deflections of the galvanometer in one direction and the other were observed. Only at the potential difference \(V = 7·5 \cdot 10^3\) volts were the latter observations not made.
Tables V, VI and VII contain the results of observations with liquid vaseline. This dielectric was not purified and was taken because there was a sufficient quantity of it. In Fig. 13 the potential distribution is represented graphically.
Table V. Liquid vaseline. \(V = +7500\) V., \(D = 31\) mm. 3·7·19.
| \(E_2\) connected with | Reading of \(E_2\) | Potential (volts) | Reading of \(E_1\) | \(E_2\) connected with | Reading of \(E_2\) | Potential (volts) | Reading of \(E_1\) | \(E_2\) connected with | Reading of \(E_2\) | Potential (volts) | Reading of \(E_1\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A | 69·0 | \(7·5 \times 10^3\) | 7·4 | 3 | 41·0 | \(3·1 \times 10^3\) | 7·5 | A | 69·5 | \(7·65 \times 10^3\) | 7·5 |
| 1 | 48·5 | 3·8 | 7·4 | 1 | 55·0 | 4·6 | " | 2 | 42·0 | 3·17 | " |
| 2 | 42·7 | 3·25 | 7·5 | A | 70·0 | 7·8 | " | 4 | 28·5 | — | " |
| 3 | 42·5 | 3·20 | 7·55 | 2 | 42·5 | 3·2 | " | 6 | 36·0 | 2·70 | " |
| A | 70·0 | 7·8 | 7·5 | 4 | 36·5 | — | " | 8 | 37·0 | 2·78 | " |
| 2 | 41·0 | 3·1 | " | 6 | 39·0 | 2·95 | " | 10 | 37·3 | 2·8 | " |
| 4 | 27·5 | — | " | 8 | 40·0 | 3·02 | " | 12 | 14·0 | 1·33 | " |
| 6 | 36·5 | 2·75 | " | 10 | 38·5 | 2·9 | " | 11 | — | — | " |
| 8 | 39·5 | 2·98 | " | 12 | 26·0 | 1·98 | " | 9 | 34·5 | 2·60 | " |
| 10 | 39·5 | 2·98 | " | 11 | — | — | " | 7 | 36·8 | 2·77 | " |
| 12 | — | — | " | 9 | 36·5 | 2·75 | " | 5 | 34·0 | 2·58 | " |
| 11 | — | — | " | 7 | 39·5 | 2·98 | " | 3 | 40·0 | 3·02 | " |
| 9 | 37·0 | 2·8 | " | 5 | 36·0 | 2·70 | " | 1 | 53·0 | 4·4 | " |
| 7 | 39·8 | 3·0 | " | 3 | 42·0 | 3·17 | " | A | 70·0 | 7·8 | " |
| 5 | 32·3 | 2·4 | " | 1 | 57·5 | 4·82 | " |
Table VI. Liquid vaseline. \(V = +5·5 \cdot 10^3\) V., \(D = 31\) mm. 4·7·19.
| Time by clock | \(E_2\) connected with | Reading of \(E_2\) | Potential (volts) | Reading of \(E_1\) | Galvanometer readings, left | Galvanometer readings, right | Difference of readings | Force of current \(10^{-9}\) amp. | Note. |
|---|---|---|---|---|---|---|---|---|---|
| 5 h 55 m | \(10^3\) | 85·4 | Machine started. A connected with \(+\); galvanometer without shunt. | ||||||
| 6 h 1 m | 76·9 | Machine started. A connected with \(+\); galvanometer without shunt. | |||||||
| 12 | Machine started. A connected with \(+\); galvanometer without shunt. | ||||||||
| 14 | A | 62·0 | 5·55 | 5·5 | Machine started. A connected with \(+\); galvanometer without shunt. | ||||
| 15 | 1 | 39·0 | 2·95 | " | 75·2 | 3·9 | 30·9 | Machine started. A connected with \(+\); galvanometer without shunt. |
Continuation of Table VI.
| Time by clock | \(Э_2\), units \(e\) | Reading on \(Э_2\) | Potential (volts) | Reading on \(Э_1\) | Galvanometer reading, left | Galvanometer reading, right | Difference of readings | Current strength, \(10^{-9}\) amp. | Note |
|---|---|---|---|---|---|---|---|---|---|
| 17 | 2 | 28.0 | 2.1 | 5.5 | 7.91 | 3.9 | 30.3 | ||
| 18 | 3 | 21.0 | 1.7 | » | 75.2 | 3.7 | 29.0 | ||
| 21 | 4 | 8.0 | 1.02 | » | 78.9 | 3.3 | 25.9 | ||
| 23 | 5 | 20.7 | 1.68 | » | 75.6 | 3.5 | 27.5 | ||
| 25 | 6 | 20.0 | 1.61 | » | 79.1 | 3.4 | 26.7 | ||
| 27 | 7 | 18.0 | 1.55 | » | 75.7 | 3.3 | 25.9 | ||
| 29 | 8 | 17.2 | 1.50 | » | 79.0 | 3.4 | 26.7 | ||
| 31 | 9 | 16.3 | 1.44 | » | 75.6 | 3.4 | 26.7 | ||
| 33 | 10 | 14.2 | 1.35 | » | 79.0 | 3.2 | 25.1 | ||
| 35 | 11 | 10.4 | 1.15 | » | 75.8 | 3.3 | 25.9 | ||
| 37 | 12 | 10.0 | 1.12 | » | 79.1 | 3.4 | 27.5 | ||
| 39 | B | 0.0 | 0.0 | » | 75.6 | 3.5 | 27.5 | ||
| 41 | 12 | 10.0 | 1.12 | » | 79.1 | ||||
| 43 | 11 | 9.6 | 1.10 | » | 75.6 | ||||
| 45 | 10 | 13.2 | 1.30 | \<5.5 | 75.7 | 3.4 | 26.7 | Voltage fell slightly. | |
| 47 | 9 | 16.0 | 1.42 | 79.1 | |||||
| 49 | 8 | — | — | 75.8 | 3.3 | 25.9 | |||
| 51 | 8 | 16.8 | 1.47 | 5.5 | 3.2 | 25.1 | |||
| 53 | 7 | 17.0 | 1.48 | » | 79.0 | ||||
| 55 | 6 | 17.2 | 1.50 | » | 3.3 | 25.9 | |||
| 57 | 5 | 18.7 | 1.57 | » | 75.7 | ||||
| 59 | 4 | 14.5 | 1.36 | » | 78.9 | 3.2 | 25.1 | ||
| 7 h 1 m | 3 | 23.0 | 1.80 | » | 75.7 | 3.2 | 25.1 | ||
| 3 | 2 | 26.2 | 2.00 | » | 79.2 | 3.5 | 27.5 | ||
| 5 | 1 | 31.0 | 2.35 | » | 75.5 | 3.5 | 27.5 | ||
| 8 | A | 61.5 | 5.50 | \<5.5 | 79.2 | 3.7 | 27.5 | ||
| 9 | — | — | average | 3.44 | 27.1 | Voltage reduced to \(3.5 \cdot 10^3\) volts. |
Table VII. Liquid vaseline. \(V = +3.5 \cdot 10^3\) V., \(D = 31\) mm. 4.7.19.
| Time by clock | \(Э_2\), units \(e\) | Reading on \(Э_2\) | Potential (volts) | Reading on \(Э_1\) | Galvanometer reading, left | Galvanometer reading, right | Difference of readings, cm | Current strength, \(10^{-9}\) amp. | Note |
|---|---|---|---|---|---|---|---|---|---|
| 7 h 27 m | A | 46.5 | \(3.60 \cdot 10^3\) | 3.5 | 78.1 | 1.1 | |||
| 29 | 1 | 28.0 | 2.00 | » | 77.0 | 1.0 | 7.85 | ||
| 33 | 2 | 16.0 | 1.42 | » | 78.0 | 1.0 | » | ||
| 35 | 3 | 8.5 | 1.05 | » | 77.0 | 1.0 | » | ||
| 37 | 4 | 5.0 | 0.88 | » | 78.0 | » | » | ||
| 39 | 5 | 5.3 | 0.90 | » | 77.0 | » | » | ||
| 41 | 6 | 5.1 | 0.88 | » | 78.0 | » | » | ||
| 43 | 7 | 4.0 | — | » | 77.0 | » | » | ||
| 45 | 8 | 4.0 | — | » | » | » | » | ||
| 47 | 9 | 4.0 | — | » | » | » | » | ||
| 50 | 10 | 3.9 | — | » | » | » | » | » | |
| 52 | 11 | 2.0 | — | » | » | » | » | ||
| 54 | 12 | 1.0 | — | » | » | » | » | ||
| 56 | B | 0.0 | — | » | » | » | » | ||
| 57 | 10 | 2.0 | — | » | » | » | » | ||
| 59 | 9 | 3.0 | — | » | » | » | » | ||
| 8 h 3 m | 8 | 4.0 | — | » | » | » | » | ||
| 5 | 6 | — | — | » | ’ | » | » | ||
| 7 | 6 | 5.5 | 0.8 | » | » | » | » | ||
| 9 | 3 | 10.0 | 1.22 | » | » | » | » | ||
| 12 | 2 | 11.0 | 1.38 | » | » | » | » | ||
| 14 | 1 | 24.0 | 1.85 | » | 77.0 | » | » | ||
| 16 | A | 46.5 | 3.60 | » | 78.0 | 1.0 | 7.85 |
Tables VI and VII show that at potential differences \(V=3500\) and 5500 volts the saturation current had already been exceeded and the dielectric was in a state close to a spark discharge. The specific electrical conductivity \(k\) of liquid vaseline had the values: at \(V=3500\) volts, \(k=0.72\cdot 10^{-14}\), and at \(V=5500\) volts, \(k=2.5\cdot 10^{-14}\ \mathrm{ohm}^{-1}\ \mathrm{cm}^{-1}\).
The curves of Fig. 13 are very similar to those obtained by Zeleny1 and Child2 for gases. They testify to the applicability of the ionic theory of gaseous conduction to liquid dielectrics.
For comparison of the potential distributions with a positive and a negative charge of the insulated electrode, only one experiment was carried out. The arrangement of the apparatus was the same as in Fig. 12; only, instead of the measuring condenser with 12 fixed probes, a condenser with one movable probe, shown in Fig. 3, was used. The readings of electrometer \(Э_2\) were not very stable, probably because only one Leyden jar was connected. The results of the observations are presented in Table VIII and shown graphically in Fig. 14.
Table VIII. Liquid vaseline. \(V=\pm 8200\) V.; \(l=31\) mm. 1·7·19.
| +8200 V. Distance from charged electrode (mm) | +8200 V. Reading on \(Э_2\) | +8200 V. Potential (volts) | −8200 V. Distance from charged electrode (mm) | −8200 V. Reading on \(Э_2\) | −8200 V. Potential (volts) |
|---|---|---|---|---|---|
| 2 | 63 | \(5.75\times 10^3\) | 15 | 52.5 | \(4.3\times 10^3\) |
| 5 | 45—50 | \(3.75\times 10^3\) | 10 | 53.5 | \(4.45\times 10^3\) |
| 10 | 42—46 | \(3.60\times 10^3\) | 5 | 54.0 | \(4.5\times 10^3\) |
| 15 | 40 | \(3.0\times 10^3\) | 0 | \(\simeq 71\) | \(\simeq 8.2\times 10^3\) |
| 20 | 35—40 | \(2.8\times 10^3\) | 20 | 50 | \(4.05\times 10^3\) |
| 25 | 34 | \(2.55\times 10^3\) | 25 | 49 | \(3.9\times 10^3\) |
| 27 | 32.5 | \(2.45\times 10^3\) | 2 | 60 | \(5.6\times 10^3\) |
| 31 | 0 | 0 | |||
| 0 | \(\simeq 71\) | \(\simeq 8.2\times 10^3\) | |||
| 15 | 40—45 | \(3.2\times 10^3\) |
In this experiment it was especially noteworthy that, when the probe was brought near the grounded electrode, a spark jumped between the probe and the electrode, which was the reason for the absence of observations near the electrode. The spark visibly convinced us that the potential drop near the electrodes was very large.
The curve for \(-V\) (Fig. 14) is almost symmetrical, whereas the curve for \(+V\), similarly to the curves of Fig. 13, has a more rapid fall of potential at the positive electrode than at the grounded one. This leads to the conclusion, though one still requiring verification, that the mobility of negative ions is greater than the mobility of positive ions.
I express great gratitude to my pupil, a student of the Siberian Higher Women’s Courses, V. M. Kudryavtseva, for the assistance rendered to me in the investigations described.
Tomsk.
—Physical Laboratory—
of the Technological Institute.
1919.
Article by Prof. V. D. Kuznetsov.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Electroscope
Voltage
Deflection in divisions
Fig. 6.
Transformer oil.
$V = +856;$ $D = 34\ \mathrm{mm}.$
Vertical axis: potential.
Horizontal axis: distance $d$ (mm).
Fig. 7.
Water.
$D = 16\ \mathrm{mm}.$
Vertical axis: potential.
Horizontal axis: distance $d$ (mm).
In Fig. 13, the vertical labels read: “Potential,” \(+\), \(−\), and \(\pi\).
In Fig. 14, the horizontal axis is labeled \(d\) (mm).
Bottom caption of Fig. 13:
Distance \(d\) between the probes and electrode \(A\) (mm).