RU2137209C1 - Device for detection of circulation of intensity vector of electric and magnetic field - Google Patents

Abstract

FIELD: electrical engineering. SUBSTANCE: device has variable resistor 9, gate 1, first and second stationary contacts (11 and 4), first and second mobile contacts (10 and 5), board 16, which has drawing of movement paths, board pointer 15, which is mounted on slide of resistor 9, high rod 12, which serves as infinitely high conductor and is mounted in perpendicular to board, ball 13, which is mounted on high rod and serves as point charge, mobile rest 14, which carries one end of resistor 9, and current-conducting rod 7, on which slide of variable resistor moves, mobile sleeve 6, which covers high rod and carries another end of resistor 9. One end of sleeve 6 carries first mobile contact 10. Its another end carries second mobile contact 5, current source 2 and ammeter 3. EFFECT: increased functional capabilities. 4 dwg

Description

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

а также вектора напряженности электрического поля

необходимо иметь источник поля и измеритель его в соответствующих точках конутра обхода.To determine the circulation of the magnetic field vector

as well as the electric field vector

it is necessary to have a source of the field and its meter at the corresponding points of the circumference loop.

Известен способ демонстрации электрического поля [5]. На основе этого способа можно построить устройства для создания электрических полей в жидком прозрачном электролите. Однако, этот способ не предусматривает определения циркуляции вектора

Из перечисленных литературных источников видно, что для создания магнитного или электрического поля, а затем определения циркуляции как вектора

так и вектора

требуется сложное и дорогостоящее оборудование. Однако, сложные измерения в магнитном и электрическом поле можно заменить простым экспериментом, т.е. использовать математическое моделирование.Known devices for creating and measuring electromagnetic fields, which are described in [1], [2] and [3]. There is also a stand for demonstrating the properties of a magnetic field [4], in which one can demonstrate various properties of a magnetic field, however, it is impossible to determine the circulation of a vector

A known method of demonstrating an electric field [5]. Based on this method, it is possible to build devices for creating electric fields in a liquid transparent electrolyte. However, this method does not provide for determining the circulation of the vector

From the listed literature sources it is seen that to create a magnetic or electric field, and then determine the circulation as a vector

so and vector

complex and expensive equipment is required. However, complex measurements in a magnetic and electric field can be replaced by a simple experiment, i.e. use mathematical modeling.

Целью изобретения является расширение функциональных возможностей известного устройства.Closest to the proposed device is a linear potentiometer, which is used in a DC circuit [6]. The resistance of the potentiometer when moving the slider (moving contact) will change according to the linear law R = γr, where γ is the proportionality coefficient, and r is the distance from the beginning of the potentiometer (fixed contact) to the slider. This device allows you to simulate only the dependence R = f (r), and does not allow you to simulate the dependence of the magnetic field strength of an infinitely long conductor with current, the dependence of the electric field strength of a point charge, as well as the dependence of the point charge potential on the distance to them. Therefore, vector circulation cannot be calculated.

The aim of the invention is to expand the functionality of the known device.

 This goal is achieved by the following: key; first and second fixed contact; tablet with the image of the bypass contours; a point indicator on the tablet, mounted on the slider of a variable resistor; a high rod simulating an infinite current conductor and fixed perpendicular to the tablet; a ball mounted on a high rod and simulating an electric point charge; a movable support on which one end of the variable resistor is fixed; a movable sleeve mounted on a high rod and on which the other end of the variable resistor is fixed; a first movable contact mounted at one end of the movable sleeve; a second movable contact mounted on the other end of the movable sleeve; a conductive rod on which the variable resistor slider moves, fixed at one end with a movable support, and connected at the other end to a second movable contact; a current source connected by a negative terminal via a key, a first fixed contact and a first movable contact with a fixed contact of a variable resistor; an ammeter connected by one terminal to the positive terminal of the current source, and the second terminal through the second fixed contact and the second movable contact with the conductive rod.

 In FIG. 1, 2 and 3 are drawings explaining the principle of operation of the proposed device. In FIG. 4 shows a General view of the proposed device.

 The proposed device (Fig. 4) contains: 1 - key; 2 - current source; 3 - ammeter; 4 - second fixed contact; 5 - second movable contact; 6 - movable sleeve; 7 - conductive rod; 8 - slider; 9 - variable resistor; 10 - the first movable contact; 11 - the first stationary contact; 12 - high rod, simulating an endless conductor with current; 13 - ball simulating an electric charge; 14 - movable support; 15 - pointer points on the tablet; 16 is a tablet with the image of the bypass circuits.

The dependence of the magnetic field H on the distance r to the conductor with current I is described by the following expression:
H = I / 2πr (1)
The dependence of the potential φ of the electric field E on the distance r to the point charge q has the form
φ = q / 4πε _o r, (2)
where ε _o is the dielectric constant.

The electric field E generated by a point charge is related to the potential φ by the following relationship:
E = φ / r (3)
The dependence of the resistance R on the distance r to one of the fixed contacts of the variable resistor (Fig. 1) has the form R = γr, where γ (Ohm / m) is the proportionality coefficient. In turn, the current J flowing under the influence of the EMF of the current source ε through the variable resistor depends on the variable resistance R and, accordingly, on the distance r.

J = ε / R = ε / γr (4)
From the expressions (1), (2) and (4) it can be seen that different physical phenomena are described by the same mathematical expressions, i.e. have an inverse proportional dependence of H, φ and J on the distance r. Therefore, in the proposed device, the complex phenomena of creating and measuring a magnetic and electric field are replaced by a simple device simulating the dependence of current J on distance r.

We will use expression (4) as a mathematical model of expressions (1) and (2). Find the relationship between the current J, measured by ammeter A (Fig. 1), and the simulated magnetic field strength H. To do this, we exclude the parameter r from expressions (1) and (4), then we obtain
H = IγJ / 2πε = K ₁ J, (5)
where K ₁ = Iγ / 2πε (1 / m) is the coefficient of proportionality.

If we put K ₁ = 1, then we can determine the value of the simulated current in a conductor of infinite length l = 2πε / γ. In this case, the readings of the ammeter J (A) will correspond to the magnitude of the magnetic field strength H (A / m).

 Thus, changing the distance r from point 0 (Fig. 1), the resistance R of the variable resistor changes, the current J measured by the ammeter A changes, respectively, the magnetic field strength H changes according to the law (5), and finally, with the help of the variable resistor ( Fig. 1) we model the dependence of the magnetic field H on the distance r to the conductor with current I, defined by the expression (1).

A variable resistor (Fig. 1) can also be used to model dependence (2). Eliminating the parameter r from expressions (2) and (4), we obtain the relationship between the current J measured by ammeter A and the simulated potential φ of the electric field of a point charge q, then we obtain
φ = (qγ / 4πε _o ε) J = K ₂ J, (6)
where K ₂ = qγ / 4πε _o ε (Ohm) is the coefficient of proportionality.

If we put K ₂ = 1, then we can determine the value of the modeled point charge q = 4πε _o ε / γ. In this case, the reading of the ammeter will correspond to the value of the potential φ (in).

 By changing the distance r from point 0 (Fig. 1), the resistance R of the variable resistor changes, the current J, measured by the ammeter A, changes, respectively, according to the law (6), the potential of the electrostatic field φ. Thus, using a variable resistor (Fig. 1), we model the dependence of the potential φ on the distance r defined by expression (2).

 Since the intensity E and the potential φ of the electrostatic field are related by dependence (3), in this model it is also possible to simulate the dependence of the electric field strength E on the distance to the point charge q.

по произвольному замкнутому контуру L. В точке А (фиг. 2) контура обхода L вектор

направлен по касательной к магнитной силовой линии (изображена пунктирной линией) и, соответственно, перпендикулярен радиус-вектору

проведенному из точки 0, где расположен бесконечный проводник с током I. Ток I направлен перпендикулярно рисунку к нам.Let's consider how vector circulation is determined in this device

along an arbitrary closed loop L. At point A (Fig. 2) of the loop L, the vector

directed tangentially to the magnetic field line (shown by a dashed line) and, accordingly, is perpendicular to the radius vector

drawn from point 0, where an infinite conductor with current I is located. Current I is directed perpendicular to the picture to us.

направлен из точки А по направлению обхода контура L. На фиг. 2 видно, что проекция

на направление

равна dS = dL cos α, где α - угол между векторами

С другой стороны dS = Rdφ, где dφ - центральный угол, под которым виден элемент

контура из точки 0, тогда dl cos α = Rd φ. С учетом этого выражение циркуляции вектора

имеет вид:

Если интервал углов от 0 до 2π разбить на конечное число m равных углов Δφ = 2π/m, то интеграл (7) можно заменить суммой

Из выражения (8) следует, что для определения циркуляции вектора

по произвольному контуру L необходимо разбить интервал углов от 0 до 2π на m равных углов Δφ из радиусов, исходящих из точки 0 (фиг. 2). В каждой i-ой точке контура L измерить напряженность магнитного поля H_i, а также соответствующий радиус R_i, проведенный в i-ю точку из точки 0. Вычислить сумму произведений H_iR_i, а затем умножить на 2π/m.
Циркуляция вектора

вычисленная по формуле (8), с высокой точностью совпадает со значением, которое можно получить по теоретической формуле

где I - моделируемый ток, протекающий по бесконечно длинному проводнику.Contour element vector

directed from point A in the direction of going around circuit L. In FIG. 2 shows that the projection

to direction

equal to dS = dL cos α, where α is the angle between the vectors

On the other hand, dS = Rdφ, where dφ is the central angle at which the element is visible

contour from point 0, then dl cos α = Rd φ. With this in mind, the expression of the circulation of the vector

has the form:

If the interval of angles from 0 to 2π is divided into a finite number m of equal angles Δφ = 2π / m, then integral (7) can be replaced by the sum

From the expression (8) it follows that to determine the circulation of the vector

along an arbitrary contour L, it is necessary to divide the interval of angles from 0 to 2π into m equal angles Δφ from radii starting from point 0 (Fig. 2). At each i-th point of the circuit L, measure the magnetic field strength H _i , as well as the corresponding radius R _i drawn to the i-th point from point 0. Calculate the sum of the products H _i R _i , and then multiply by 2π / m.
Vector Circulation

calculated by the formula (8), with high accuracy coincides with the value that can be obtained by the theoretical formula

where I is the simulated current flowing along an infinitely long conductor.

по произвольному замкнутому контуру L. В точке А (фиг. 3) контура L вектор

направлен по силовой линии и исходит из положительного точечного электрического заряда q. Вектор элемента контура обхода

направлен из точки А по направлению обхода контура L. На фиг. 3 видно, что проекция

на направление вектора

равна dr = dl cosα, где α - угол между векторами

. Учитывая выражение (3) для бесконечно малого приращения расстояния dr, получим бесконечно малое приращение потенциала dφ = Edr, тогда циркуляция вектора

имеет вид:

Проведем из центра расположения точечного заряда q радиусы до пересечения с контуром обхода L. При этом, радиусы должны образовать m равных углов в интервале углов от 0 до 2π, тогда интеграл (10) можно заменить суммой конечных приращений Δφ_i потенциала

где Δφ_i= φ_i+1-φ_i, i = 1, 2, 3, ..., m (12)
Из выражения (11) следует, что для определения циркуляции вектора

необходимо на контуре обхода выбрать m точек, в которых будет измеряться потенциал φ_i, i = 1, 2, 3, ..., m. По измеренным потенциалам определяем конечные приращения Δφ_i по формуле (12) и определяем их сумму по формуле (11).Consider how vector circulation is determined

along an arbitrary closed circuit L. At point A (Fig. 3) of circuit L, the vector

directed along the line of force and proceeds from a positive point electric charge q. Bypass contour element vector

directed from point A in the direction of going around circuit L. In FIG. 3 shows that the projection

to the direction of the vector

equal to dr = dl cosα, where α is the angle between the vectors

. Given expression (3) for an infinitesimal increment of the distance dr, we obtain an infinitely small increment of the potential dφ = Edr, then the circulation of the vector

has the form:

Draw the radii from the center of the point charge q to the intersection with the bypass contour L. Moreover, the radii must form m equal angles in the range of angles from 0 to 2π, then the integral (10) can be replaced by the sum of the finite increments Δφ _{i of the} potential

where Δφ _i = φ _{i + 1} -φ _i , i = 1, 2, 3, ..., m (12)
From the expression (11) it follows that to determine the circulation of the vector

it is necessary on the bypass path to select m points at which the potential φ _i , i = 1, 2, 3, ..., m will be measured. From the measured potentials, we determine the final increments Δφ _i by the formula (12) and determine their sum by the formula (11).

Когда обучаемый определяет циркуляцию вектора

то полагает, что поле создается и есть измеритель соответствующей характеристики поля. В итоге он измеряет величину напряженности H или потенциала φ по амперметру в соответствующей точке контура обхода.The proposed device operates as follows. When the key l is turned on in a closed circuit, current flows from the positive terminal of the current source 2, through the ammeter 3, the second fixed contact 4 and the second movable 5 contact of the movable sleeve 6, the conductive rod 7, the slider 8 of the variable resistor 9, the variable resistor 9 itself, the first movable 10 contact of the movable sleeve 6, first fixed 11 contact, key l to the negative terminal of the current source 2. Ammeter 3 shows the current value, which is determined by the expression (4), i.e., the current value is inversely proportional to the distance r from the high rod 12, m delirium infinite conductor carrying a current I, or from the center of the ball 13, fitted on a high rod 12 which simulates a point charge q. The movable sleeve 6 is mounted on a high rod 12 and is rigidly connected through a conductive rod 7 and a variable resistor 9 with a movable support 14. The slider 8 of the variable resistor is provided with a pointer 15 points on the tablet 16. The tablet shows the bypass contours with points where it is necessary to measure the magnetic intensity field according to the formula (5) or the potential of the electrostatic field according to the formula (6). Rotating a linear variable potentiometer around a high rod 12 or ball 13, as well as moving the slider 8 with pointer 15, we find the desired point on the bypass path of tablet 16 and measure H or φ at this point. According to the algorithm (8) or (11) we find, respectively, the circulation of the vector

When the learner determines the circulation of the vector

he believes that the field is being created and is a measure of the corresponding field characteristics. As a result, he measures the magnitude of the tension H or potential φ by an ammeter at the corresponding point of the bypass circuit.

не уменьшает познавательной возможности, т.к. на установке (модели) обучаемый проводит те же операции, которые проводил бы на натуре.The proposed device for determining the circulation of the vector

does not reduce cognitive ability, because on the installation (model), the student carries out the same operations that he would conduct in kind.

 The technical and economic efficiency of the proposed device lies in the fact that the range of use of the device is expanding, which ensures an improvement in the quality of assimilation of the basic laws of physics by students.

 The proposed device is implemented at the Department of Physics and is used in the educational process for laboratory work on electromagnetism.

Literature:
1. G. A. Ryazanov. Experiments and modeling in the study of electromagnetic fields. Science, M., 1966.

 2. G.A. Ryazanov. Electrical modeling using vortex fields. Science, M., 1969.

 3. F. V. Kushnir et al. Measurements in communication technology. Communication, M., 1970, p. 385,470.

 A stand for demonstrating the properties of a magnetic field. USSR, auth. N 1720074, 03/15/92, bull. ten.

 5. A method of demonstrating an electric field. USSR, auth. N 1603424, 10.30.90, bull. 40.

 6. A. S. Greenberg. Function generation using potentiometers. Energy, M., 1965, p. 149, fig. 8.13.

Claims (1)

 A device for determining the circulation of the vector of electric and magnetic field strengths, containing a variable resistor, characterized in that a key, a first and second fixed contact, a tablet with the image of the bypass circuits, a point indicator on the tablet, mounted on the variable resistor slider, a high rod, are inserted into it; simulating an infinite current conductor and fixed perpendicular to the tablet, a ball mounted on a high rod, simulating an electric point charge, a movable support on which one end of the variable resistor is mounted, a movable sleeve mounted on a high rod and on which the other end of the variable resistor is fixed, a first movable contact mounted on one end of the movable sleeve, a second movable contact mounted on the other end of the movable sleeve, a conductive rod on which to move a slider of a variable resistor and fixed at one end with a movable support, and the other end connected to a second movable contact, a current source connected by a negative terminal through a key, p rvy fixed contact and first movable contact with the stationary contact of the variable resistor, an ammeter, one terminal connected to the positive terminal of the current source and the second terminal via the second fixed contact and second movable contact with a conductive rod.

Images