3.6. Vector of electric displacement

Intensity of the electrostatic field depends on the dielectric permittivity of a medium. On the Fig. 7 we can see the field of infinite plate in different dielectrics (₃₁₂). On boundary of two dielectrics a value of an electric intensity has step-wise changes.

Fig. 7 – Vector of electric intensity in different dielectrics	Fig. 8 – Vector of electric displacement in different dielectrics

The quantity that doesn't depend on the properties of a medium, is the vector of electric displacement , that is related with the intensity vector for isotropic medium as

. (18)

Substituting (4) in (18) we obtain vector of electric displacement for the field of the point charge q₁ at r distance from it

On the Figure 8 is represented the image of vector of electric displacement for the infinite plate field in different dielectrics (₃₁₂). On the bounds of dielectric the electric displacement vector lines doesn't interrupt. Electric displacement vector is introduced formally and is an auxiliary quantity.

4. Description of laboratory research facility and methodology of measurements

Devices and outfits: voltage source e, potentiometer P, voltmeter V, microamperemeter mA, set of electrodes A and B, cell with electrolyte and conducting paper a-b-c-d, probe C.

Study of electrostatic field is in finding of the magnitude and direction of intensity in any point. Thus, the problem brings to the construction of field lines. It's experimentally hard to define the direction of field lines. It is easier to find distribution of potentials and to define position and form of equipotential surfaces.

For studying the distribution of potentials in electrostatic field there is used a probe - an electrode, which is entered in explored point of the field. The probe connected to device, which measures potentials difference between the probe and the point of the field, where potential is taken to be zero. It is necessary that the presence of the probe doesn’t break the observable field and receive the potential of that point, in which it is located.

Studying of electrostatic field is difficult to make the experimentally, as there in nonconductive medium can’t happen automatic potentials equalizing of the fields' point and the probe. To make this equalizing happen, we should provide runoff of the charges from the probe. In addition, for measuring the potential difference between the points of electric field it is needed to use electric devices (electrometers). That's why the studying of electrostatic field is replaced by the studying of the direct current field. Studying method of electrostatic field by initiation of another equivalent field is called modeling.

For accomplishment of electric field and its exploring, we mount the circuit, which is shown on the Fig. 9, where A and B ̵ electrodes, that create an observable field; C ̵ an electrode-probe, with the help of which the field researches; P ̵ potentiometer for voltage regulation; V ̵ voltmeter; μA ̵ microamperemeter.

Fig. 9 – Installation diagram of lab 2-1 equipment

On the paper abcd, whetted in the diluted solution of electrolyte, put electrodes A and B, connected to the poles of the current source.

As specific conductivity of this paper is in a lot of times less than specific conductivity of electrodes, so the electric current field between electrodes A and B equivalent to electrostatic field. In the work, we find not the position of equipotential surfaces, but lines of their intersection with the plane abcd.

Let the potentials of electrodes be equal _A and _B and, as it shown on the Fig.9, _A< _B as electrode B connected to the plus terminal of the source. Suppose, the potential of electrode A, connected to minus terminal, equals zero (_A = 0

In order to build an equipotential line with potential ₁ with the help of potentiometer P set on the voltmeter potential difference, which is equals ₁. Voltmeter measures potential difference between points D and K, _D ̵ _K. But _K=_A=0. It means, that voltmeter measures the value of potential in the point D. It's evident, that . If to touch with a probe an electrode A, then , and current through the microampermeter will begin to flow from point D to a point A. If to touch with a probe an electrode B, then , and current through the microampermeter will begin to flow in other side - from a point B to point D.

That's why between the electrodes we can always find such point M, which potential will be equal _D=₁. If we put the probe C in this point, there will be no current through ampermeter, as _D=_M=₁. With unchanging voltage on a voltmeter, we find 8 ̵ 10 points, potential in which equals ₁, by getting absence of a current in the ampermeter. When we unite found points with the line, we’ll have an equipotential line with potential ₁. In order to build the line with potential ₂ we move D, set the voltage on a voltmeter equal ₂ and by the foregoing method find the points with potential ₂.

Equipotential lines have to be built in such way, that potentials differences between any near-neighboring lines were the same. For example, to build five equipotential lines we should divide the potential difference U between electrodes A and B on 6 equal parts. When we set on the voltmeter ₁=U/6, we must find the line with this potential. Second line must have potential ₂=2₁, third – ₃=3₁ etc. Surface of electrode A has a potential ₀=0, and surface of electrode B has a potential ₆=U.

Next we can bield a field lines. Field lines build perpendicular to equipotential lines, including electrodes. Field lines start on the positive electrode, and finish on the negative. Field lines must be built in such way, that their density was proportional to the field intensity.

If to measure potentials ₁ and ₂ two points which lay on one field line on small distance r from each other by formula (17) it is possible to calculate an electric intensity in a point which is in the middle between points with potentials ₁ and ₂. For this purpose the probe C should be put in the point 1 chosen on a field line and by rotation of handle of potentiometer P to achieve lack of a current in the microampermeter. Thus voltage measure observations will be equal to value of a potential of this point ₁. Then it is necessary to put a probe C in the point 2 chosen on the same field line and by rotation of handle of potentiometer P to achieve lack of a current in the microampermeter. Thus voltage measure observations will be equal to value of a potential of this point ₂. Having metered distance between these points Dr, using formulae E=(₂–₁)/r it is possible to calculate an electric intensity vector value. The electric-field vector direction is spotted in a field line direction.

If points 1 and 2 coincide with intersections of a field line with two next equipotential lines, then (₂–₁) will correspond to a potential difference between the neighbour equipotential lines =₁. Thus, for calculation of absolute value of an electric intensity it is necessary to measure only distance r between points 1 and 2 (distance between the neighbour equipotential lines).