RU2479868C1 - Plant for investigation of stationary electric field - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: plant comprises: a switch for two positions for connection to a voltmeter with high input resistance or a single probe, or a double probe with a pointer, a set of detachable various pairs of conducting buses, which model various flat electric fields; screws with nuts installed on a pad with electroconductive paper for fixation of a pair of detachable conductive buses; a central screw with a nut, installed on a pad with electroconductive paper in the middle between the pair of detachable conductive buses; a template from a dielectric with a working edge corresponding to the profile of the bypass contour, fixed on the pad with electroconductive paper with the help of the central screw with the nut; a set of detachable various templates from dielectric, which model various bypass contours. A movable ruler with one end is fixed on a runner moving along a fixed stem in parallel with an axis Y, and its second side lies on the fixed ruler. Besides, the plant comprises a pad with a document sheet and a system of coordinates similar to the one installed on the pad with electroconductive paper.

EFFECT: increased accuracy of performed experiments.

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Description

The invention relates to educational devices and can be used in laboratory practice in higher and secondary special educational institutions at the rate of physics to obtain and deepen knowledge of physical laws and phenomena.

A device is known for measuring potentials and building isopotential lines (G. A. Ryazanov. Experiments and modeling in the study of electromagnetic fields. Publishing House "Science". M., 1966, p.77, Fig. 7.2). Using a measuring needle (single probe), it is possible to find points with a given potential on it and build isopotential lines. To measure the potential, a bridge circuit is used. By setting the rechord slider to the division corresponding to the given potential, we move the needle along the surface of the tablet with electrically conductive paper, achieving the disappearance of current in the bridge. By pressing the needle through the carbon paper on the document sheet, we fix a number of points. Then we remove the document sheet from under the copy paper, connect the obtained points with a smooth curve and get isopotential lines with the given potentials. Rapid wear of the electrically conductive and carbon paper is observed, as well as the low accuracy of the experiment.

A device is also known for directly measuring the potential difference recorded by a double probe (ibid., P. 75, Fig. 7.1). This device also uses a bridge circuit and carbon paper with a document sheet, which is inconvenient during the experiment. Inaccurate measurements of the dependence of the potential and, accordingly, of the electric field along the field line are obtained. There is a rapid wear of the electrically conductive and carbon paper, as well as low accuracy of the experiment.

Closest to the proposed installation is a device for researching a stationary electric field (RU patent No. 2284581. Bull. No. 27 dated 09/27/2006. Authors: Belokopytov R.A. and Kovnatsky V.K.) (Fig. 1). It contains a direct current source, a double probe with an arrow, a tablet with electrically conductive paper, a pair of removable conductive buses mounted on electrically conductive paper and connected to the terminals of a direct current source, a set of removable various pairs of conductive buses simulating different flat electric fields, screws with nuts, mounted on a tablet with electrically conductive paper for mounting a pair of removable conductive tires, a central screw with a nut mounted on a tablet with electrically conductive paper in the middle between the steam of removable conductive busbars, a dielectric pattern with a working edge corresponding to the bypass profile, fixed on a tablet with electrically conductive paper using a central screw with a nut, a set of various removable dielectric patterns, simulating various bypass contours, a voltmeter with a large input resistance, the first input which is connected to the first needle of the double probe with an arrow.

This setup allows you to create various flat electric fields and explore them. It can experimentally confirm the Gauss theorem for the electrostatic field, as well as the theorem on the circulation of the electric field intensity vector. Using this double probe with an arrow, one can demonstrate the course of power and equipotential lines. At any point in the field, one can find the direction of the electric field strength, the gradient of the potential, and other characteristics of the field.

However, on this installation you can only demonstrate the appearance of equipotential lines, but you cannot remember them on a document sheet, fix the coordinates of these points and then use them to construct electric field lines and calculate the field strength and its gradient. If you use carbon paper and a document sheet, this will complicate the installation, it will take additional time to remove, install carbon paper and a document sheet and process the results. Non-economical consumption of electrically conductive and carbon paper will be observed, as To obtain a point on the document sheet through the copy paper, it is necessary not to touch the double probe with the needles, but to press strongly on the electrically conductive paper, which quickly becomes unusable. To conveniently and quickly find the coordinates of the potentials, it is also necessary to have a single probe.

The technical result of the invention is to improve the accuracy of experiments.

The specified technical result is achieved by the fact that in a known installation for studying a stationary electric field containing a direct current source, a double probe with an arrow, a tablet with electrically conductive paper, a pair of removable conductive buses mounted on electrically conductive paper and connected to the terminals of the direct current source, a voltmeter with a large input impedance, the first input of which is connected to the first needle of the double probe with an arrow, a set of removable various pairs of conductive buses simulating different flat electric fields, screws with nuts installed on a tablet with electrically conductive paper for attaching a pair of removable conductive tires, a central screw with a nut mounted on a tablet with electrically conductive paper in the middle between a pair of removable conductive tires, a dielectric piece with a working edge corresponding to the profile of the bypass contour fixed on a tablet with electrically conductive paper using a central screw and nut, a set of removable various dielectric patterns that simulate various bypass contours, agrees The invention introduced a single probe, the needle of which is connected to the first needle of the double probe with an arrow, a two-position switch, the common contact of which is connected to the second input of the voltmeter with a large input resistance, its first contact is connected to one of the removable conductive spike, and its second contact - with the second needle of a double probe with an arrow, a fixed ruler fixed on a tablet with electrically conductive paper parallel to one of its sides, which acts as the Y axis of the Cartesian coordinate system, not a rod mounted on the opposite side of the tablet with electrically conductive paper parallel to the fixed ruler, a slide moving on the fixed rod, a movable ruler fixed at one end to the slider, and its second end lies on the fixed ruler, which acts as the X axis of the Cartesian system coordinates, a tablet with a document sheet with an image of a coordinate system similar to that installed on a tablet with electrically conductive paper.

Figure 1 shows a prototype; figure 2 is a General view of the proposed installation; figure 3-9 - drawings explaining the principle of its operation.

The proposed installation (figure 2) contains: 1 - tablet with electrically conductive paper; 2 - screws with nuts; 3 - a pair of removable conductive tires; 4 - a set of removable various pairs of conductive tires; 5 - a direct current source; 6 - central screw with nut; 7 - patterns from a dielectric; 8 - a set of removable various patterns of a dielectric; 9 - voltmeter with a large input resistance; 10 - a double probe with an arrow; 11 - single probe; 12 - switch to two positions; 13 - fixed ruler (Y axis); 14 - fixed stock; 15 - engine; 16 - movable ruler (X axis); 17 is a tablet with a document sheet.

Consider how the proposed installation is used. It includes a tablet with electrically conductive paper 1, on which screws with nuts 2 are installed for attaching a pair of removable conductive buses 3. To form a variety of flat electric fields, we use a set of different pairs of removable conductive buses 4. The pair of removable conductive buses 3 used is connected to the source terminals DC 5. In the middle between a pair of removable conductive busbars 3, a central screw with a nut 6 is installed for fastening the patterns of the dielectric 7 with a working edge corresponding to the profile of the bypass circuit. A digital marking equal to the measurement step is applied to the dielectric 7 pattern and there is a hole for the central screw with nut 6. To simulate a variety of bypass contours in a flat electric field, we use a set of removable various dielectric patterns 8. When measuring potentials and potential differences between points, we use a voltmeter with a large input resistance 9, the first input of which is connected to the first needle of the double probe with arrow 10. To determine the potential and build lines of equal potential, we use a single probe 11, the needle of which is connected to the first needle of the double probe with arrow 10.

The operation mode is switched from a single probe 11 to a double probe with an arrow 10 using a two position switch 12, the common contact of which is connected to the second input of the voltmeter with a large input resistance 9, its first contact is connected to one of the removable conductive buses 3, and the second contact with the second needle of the double probe with arrow 10.

To determine the coordinates of a point on a tablet with electrically conductive paper 1, we use a fixed ruler 13 mounted on a tablet with electrically conductive paper 1 parallel to one of its sides, which acts as the ordinate axis "U" of the Cartesian coordinate system.

To implement the X axis of the Cartesian coordinate system on the opposite side of the tablet with electrically conductive paper 1, a stationary rod 14 is mounted parallel to the fixed ruler 13, on which the slider 15 is located. The movable ruler 16 is fixed at one end to the slider 15 moving along the movable rod 14, and its second end lies on a fixed ruler 13. The movable ruler 16 acts as the abscissa axis “X” of the Cartesian coordinate system.

на заданное направление. Укрепив на планке из изолятора на небольшом расстоянии l друг от друга два металлических острия, получим двойной зонд с постоянной базой (база - расстояния между иглами, будем считать ее равной шагу измерений). Если база зонда l достаточно мала, а силовые линии не слишком искривлены, то стационарное поле в окрестности зонда можно считать однородным. При этом условии проекция напряженности электрического поля E_l в средней точке зонда на прямую, проходящую через его иглы (фиг.3), связана с напряжением между иглами U следующим выражением:During the experiment, it is necessary to determine the projection of the vector

to a given direction. Having fixed two metal tips on the bar from the insulator at a small distance l from each other, we get a double probe with a constant base (the base is the distance between the needles, we will consider it equal to the measurement step). If the base of the probe l is small enough and the field lines are not too curved, then the stationary field in the vicinity of the probe can be considered homogeneous. Under this condition, the projection of the electric field strength E _l at the midpoint of the probe onto a straight line passing through its needles (Fig. 3) is related to the voltage between the needles U by the following expression:

Figure 3 circles show the needles of the probe. Arrow A indicates the direction in which the vector is projected.

на заданное направление необходимо условно отметить на зонде (стрелка А) положительное направление. Например, за положительное направление принимаем красный подводящий к игле провод. Знак на табло вольтметра с большим входным сопротивлением 9 будет указывать на знак проекции E_l.To determine the sign of the projection

for a given direction, it is necessary to conditionally mark a positive direction on the probe (arrow A). For example, for the positive direction we take the red wire leading to the needle. The sign on the board of the voltmeter with a large input resistance of 9 will indicate the sign of the projection E _l .

Consider how the proposed installation (figure 2) experimentally confirms the Gauss theorem. To do this, set the switch to two positions 12, set to the second position "Double probe" (DZ). In this case, a double probe with an arrow 10 is connected to the input of the voltmeter 9.

Choose from a set of removable various pairs of conductive tires 4 the necessary pair of removable conductive tires 3 and put them on a tablet with electrically conductive paper 1. We fix the bus 3 with screws and nuts 2 and connect the bus 3 with a DC source 5. Figure 4 shows for As an example, the lines of force of an electric field, which is modeled using a selected pair of removable conductive buses 3. Choose from the set of removable various patterns from dielectric 8 the desired pattern 7, put it on a tablet with electrically conductive paper 1 and fix it with a cent cial screw with nut 6. At the patterns of dielectric material 7 numerals indicate the investigated point of the electric field. These points are placed in increments equal to the base of the double probe 10, the terminals of which are connected to the inputs of the voltmeter with a large input resistance 9. The voltmeter 9 must have a large input resistance so as not to distort the structure of the investigated electric field.

In accordance with the Gauss theorem for an electrostatic field in vacuum: the flow of electrostatic field intensity through an arbitrary closed surface S is equal to the ratio of the algebraic sum of the electric charges covered by this surface to the electric constant ε ₀

всюду параллелен основаниям полученного цилиндра, то интегрирование выражения E_ndS нужно произвести только по его боковой поверхности. Разобьем цилиндрическую поверхность на N прямоугольников с высотой h и основанием dl, площадь которых равна hdl. Это позволит перейти от интегрирования по боковой поверхности цилиндра к интегрированию по его профилюThe surface S (Fig. 4) in a flat field can be represented as a cylinder cut from electrically conductive paper with a paper thickness h. Since the vector

everywhere parallel to the foundations of the resulting cylinder, the integration of the expression E _n dS should be done only on its lateral surface. We divide the cylindrical surface into N rectangles with height h and base dl, whose area is hdl. This will allow us to move from integration along the lateral surface of the cylinder to integration along its profile

через замкнутую поверхность (2) в него входит интеграл по замкнутой кривой L (фиг.4), численно равный потоку вектора

через боковую поверхность описанного выше цилиндра. Так как в однородной проводящей среде нет зарядов, то поток вектора

через этот контур должен быть равен нулю.Relation (3) expresses the Gauss theorem for a plane electric field. Instead of a vector stream

through the closed surface (2), it includes the integral over the closed curve L (Fig. 4), numerically equal to the flux of the vector

through the side surface of the cylinder described above. Since there are no charges in a homogeneous conducting medium, the flux of the vector

through this circuit should be equal to zero.

Replace the left side of expression (3) with the sum

на направлении вектора

в i-й точке контура обхода L (фиг.4),

- шаг измерений E_ni на контуре L, соответствующий этой точке. Если шаг измерений

для всех точек выбрать одинаковым, например, равным базе l двойного зонда со стрелкой 10, а значение E_ni определять по формуле (1), тогда выражение (4) приобретает видwhere E _ni is the projection of the vector

in the direction of the vector

at the i-th point of the loop circuit L (figure 4),

is the measurement step E _ni on circuit L corresponding to this point. If the measurement step

for all points, choose the same, for example, equal to the base l of the double probe with arrow 10, and determine the value of E _ni by formula (1), then expression (4) takes the form

(фиг.4). Напряжение U_i следует измерять со своим знаком, тогда интеграл (5) будет практически равен нулю. Знаки напряжения указываются на табло вольтметра с большим входным сопротивлением 9. Чем меньше база l двойного зонда со стрелкой 10, тем точнее результат.Thus, the flow of electrostatic field strength in vacuum through the surface S is found as the sum of the voltages U _i determined by a voltmeter with a large input resistance 9. In this case, a double probe with arrow 10 at each i-th point must be installed so that arrow A coincides with normal

(figure 4). The voltage U _i should be measured with its sign, then the integral (5) will be practically equal to zero. The voltage signs are indicated on the board of the voltmeter with a large input resistance 9. The smaller the base l of the double probe with arrow 10, the more accurate the result.

Let us consider how we experimentally confirm the theorem on the circulation of the electric field vector. To do this, we will examine the electric field depicted in figure 5. Take the same form of pattern 7 as in figure 4.

вдоль произвольного замкнутого контура LAccording to the vector circulation theorem

along an arbitrary closed loop L

Replace the integral (6) with the sum, then

на направлении вектора

(фиг.5), Δl_i - шаг измерений. Если шаг Δl_i на всем контуре выбрать одинаковым и равным базе зонда Δl_i=l, а значение E_li определять по формуле (1), тогда выражение (7) примет видwhere E _li is the projection of the vector

in the direction of the vector

(Fig. 5), Δl _i is the measurement step. If the step Δl _i on the entire circuit is chosen equal and equal to the probe base Δl _i = l, and the value of E _li is determined by the formula (1), then expression (7) will take the form

равна сумме напряжений U_i, измеренных вольтметром с большим входным сопротивлением 9, на контуре исследуемого лекала 7 с шагом l двойного зонда со стрелкой 10. При этом двойной зонд со стрелкой 10 в каждой i-ой точке контура лекала 7 должен устанавливаться так, чтобы стрелка А совпадала каждый раз с направлением вектора

(фиг.5) (направлением обхода). Напряжение U_i следует суммировать со своими знаками, тогда интеграл (8) будет практически равен нулю. Чем меньше будет база двойного зонда 10, тем точнее результат.From the expression (8) it can be seen that the circulation of the vector

equal to the sum of the voltages U _i measured with a voltmeter with a large input resistance 9, on the contour of the studied pattern 7 with step l of the double probe with arrow 10. Moreover, the double probe with arrow 10 at each i-th point of the contour of the curve 7 should be installed so that the arrow And each time coincided with the direction of the vector

(FIG. 5) (bypass direction). The voltage U _i should be summed with its signs, then the integral (8) will be practically zero. The smaller the base of the dual probe 10, the more accurate the result.

Consider how the lines of equal potential are built, the electric field strength is determined, as well as the direction of the gradient at any point in the field.

To build lines of equal potential (isopotential lines), we first start a document sheet and lay it on a tablet 17, which is the same size as a tablet with electrically conductive paper 1. On the tablet with a document sheet 17, put the coordinate axis "U", as shown in Fig.6, and do the markup. We use the usual ruler as the coordinate axis “X”, which can move up or down the tablet with document sheet 17. Then we unscrew the central screw with nut 6 and remove the piece from dielectric 7. This forms a clean field on the tablet with electrically conductive paper 1. The switch to two positions 12 is set to the position "Single probe" (OZ). On the instructions of the teacher or independently choose a pair of removable conductive tires 3, which will form the required electric field. We estimate how approximately the equipotential lines of the selected pair of removable conductive tires 3 look. Thus, we solve the problem of a sufficient number of experimental points that transmit the features of the equipotential lines.

Moving the single probe 11, we find the required (set) potentials on the tablet with electrically conductive paper 1. We install the single probe 11 perpendicular to the tablet with electrically conductive paper 1. Then we move the movable ruler 16 until it touches the needle of the single probe 11. Determine the "X" coordinate of this point, and from the fixed ruler 13 we determine the coordinate "U" of this point. We put this point on the tablet with document sheet 17. Then we move the movable ruler 16 up or down (for example, 1 cm) and, moving the single probe 11 along the movable ruler 16 left or right, we find the point of equal potential and determine its coordinates "X" and "U". Put the coordinates of this point on the tablet with document sheet 17. Using a series of such points on the tablet with document sheet 17, we construct an isopotential line with a given potential. Isopotential lines corresponding to different potential values are constructed in the same way.

в разных точках поля.Since the electric field lines are directed perpendicular to the isopotential lines and in the direction of decreasing potential, then, knowing the location of the isopotential lines, we can immediately imagine where the vector is directed

at different points in the field.

To determine the electric field strength at an arbitrary point on the field (Fig. 7), it is necessary to draw a segment of the field line Δl perpendicularly to the isopotential lines through it. If the potential interval Δφ is sufficiently small and the field in the vicinity of this point can be considered almost uniform (this can be judged by the shape of the isopotential lines), then, by measuring the length of the line of force Δl, we obtain the tension

направлен в сторону убывания потенциала (фиг.7) Если выбрать шаг двойного зонда со стрелкой 10 Δl=1 см и выразить Δφ в вольтах, тогда получим формулу для расчета в произвольной точке А (фиг.7) напряженностиA minus sign indicates that the tension vector

directed towards the decreasing potential (Fig. 7). If we select the step of a double probe with an arrow of 10 Δl = 1 cm and express Δφ in volts, then we will obtain a formula for calculating the tension at an arbitrary point A (Fig. 7)

At point A, you can also show the gradient of the potential, which is directed towards increasing potential.

Using equipotential lines, several electric field lines can be constructed. Among the power lines E, select one line l and select it on the tablet with document sheet 17. If you select an arbitrary power line l, as shown in Fig. 8, and take one of the pair of removable conductive buses 3 for the zero reference point, and then use single probe 11 to measure the potentials at the indicated points, then we can build the dependence of the potential φ along the field line l: φ = φ (l). At each point of the field line l, we find the electric field strength according to formula 9 and construct the dependence E = f (l).

на оси координат "X" и "У". Для этого переключатель на два положения 12 ставим в положение «Двойной зонд» (ДЗ). Разместим двойной зонд со стрелкой 10 в исходную точку на планшете с электропроводящей бумагой 1 и направим его стрелку сначала параллельно оси "X", а затем параллельно оси "У". Показание вольтметра 9 Δφ_x и Δφ_y отложим в удобном масштабе на планшете с документальным листом 17 и сложим их геометрически. Направление вектора

находим по правилу, как показано на фиг.9. Модуль вектора Е находим по формулеConsider the construction of lines of force by measuring the projections of the vector

on the coordinate axis "X" and "Y". To do this, set the switch to two positions 12 in the position of the "Double probe" (DZ). We place the double probe with arrow 10 at the starting point on the tablet with electrically conductive paper 1 and direct its arrow, first parallel to the "X" axis, and then parallel to the "Y" axis. The voltmeter 9 Δφ _x and Δφ _{y are} set aside on a convenient scale on a tablet with document sheet 17 and we add them geometrically. Vector direction

we find by the rule, as shown in Fig.9. The modulus of the vector E is found by the formula

(фиг.9), переносим двойной зонд со стрелкой 10 в его конечную точку на планшете с электропроводящей бумагой 1 и повторим измерения. Если соединить точки, в которых производились измерения плавной кривой на планшете с документальным листом 17, получим линию, близкую к искомой силовой линии (фиг.9).By constructing a segment proportional to the vector

(Fig. 9), transfer the double probe with arrow 10 to its end point on the tablet with electrically conductive paper 1 and repeat the measurement. If we connect the points at which the smooth curve was measured on the tablet with the document sheet 17, we get a line close to the desired line of force (Fig.9).

The technical and economic efficiency of the proposed installation is that it provides an increase in the quality of assimilation by students of the basic laws and phenomena of physics.

The proposed installation is implemented at the Department of Physics A.F. Mozhaysky and is used in the educational process for laboratory work on electricity.

Claims (1)

Installation for researching a stationary electric field containing a direct current source, a double probe with an arrow, a tablet with electrically conductive paper, a pair of removable conductive buses mounted on electrically conductive paper and connected to the terminals of a direct current source, a voltmeter with a large input resistance, the first input of which is connected to the first needle of a double probe with an arrow, a set of removable various pairs of conductive tires simulating different flat electric fields, screws with nuts, installed on the plan you are holding electrically conductive paper for attaching a pair of removable conductive tires, a central screw with a nut mounted on the tablet with electrically conductive paper in the middle between a pair of removable conductive tires, a dielectric piece with a working edge corresponding to the bypass profile, fixed to the tablet with electrically conductive paper using a central screws with a nut, a set of removable various dielectric patterns modeling various bypass contours, characterized in that a single probe is inserted into it, the needle of which is connected and with the first needle of the double probe with an arrow, a switch to two positions, the common contact of which is connected to the second input of the voltmeter with a large input resistance, its first contact is connected to one of the removable conductive tires, and its second contact is with the second needle of the double probe with an arrow , a fixed ruler mounted on a tablet with electrically conductive paper parallel to one of its sides, and which acts as the ordinate axis of the "Y" of the Cartesian coordinate system, a fixed rod mounted on the opposite side of the plate the one with electrically conductive paper parallel to the fixed ruler, an engine moving along the fixed rod, a moving ruler fixed at one end to the engine, and the other end of it lying on the fixed ruler, which acts as the X axis of the Cartesian coordinate system, a tablet with a document sheet with an image of a coordinate system similar to that installed on a tablet with electrically conductive paper.

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