RU2491650C1 - Installation for research of electromagnetic field of helmholtz coils - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: installation contains Helmholtz coils, which winding ends are connected to output terminals of audio-frequency generator. The coils are installed at the support having a graduated scale. A movable platform with position indicator moves along the support by means of belt drive. The measuring coil is installed at support perpendicular to it. At the support between Helmholtz coils at level of their axis there is a reference coil installed in parallel to the measuring coil. Toroidal coil is fixed at the moving rod with position indicator at a dial scale with grade divisions. There is also a phase difference metre which first inputs are connected to the system recording electromotive force and the second inputs are connected to the reference coil. Two-way bipolar switch ensures connection either of the measuring coil or toroidal coil to inputs of the system recording electromotive force and first inputs of phase difference metre.

EFFECT: expanding the research area and improving measurement accuracy.

9 dwg

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 study and deepen knowledge of physical laws and phenomena.

The Helmholtz electric rings are known, formed by two toroidal electromagnets, the windings of which are included in the alternating current circuit (G. A. Ryazanov, Electrical modeling using vortex fields. Publishing House "Science", M., 1969, p. 76, Fig. 41). On them in this form it is impossible to investigate the magnetic field generated by the electric field.

A well-known training device for the study of electromagnetic fields (RU patent No. 2210815, G09B 23/18, 08/20/2003 Bull. No. 23 Author: Kovnatsky V.K.). This device allows you to remove the dependence of the bias current on the frequency and intensity of the electric field, to determine the dependence of the magnetic field on the distance to the axis of the Helmholtz electric rings. At the same time, it is impossible to measure the electric field on it; you have to use other devices. Only the magnitude of the magnetic field vector is measured on this instrument, and the direction of the vector cannot be determined. It is also impossible to demonstrate a right-handed system between the vectors of the bias current density and magnetic field strength.

Closest to the proposed installation for studying the electromagnetic field of Helmholtz electric rings is a training device for demonstrating the second Maxwell equation (RU patent No. 2285960, G09B 23/18, 10.23.2006 Bull. No. 29 Authors: Belokopytov R.A., Kovnatsky V.K. .) (prototype). The device contains: Helmholtz electrical rings mounted perpendicular to the stand and the leads of the windings of which are connected to the output terminals of the sound frequency generator; a movable platform moving along a stand between Helmholtz electric rings along the scale with divisions; a measuring coil mounted on a movable platform at the level of the axis of the Helmholtz electric rings and an equal distance from them so that the axis of the measuring coil is perpendicular to the stand; pointer position measuring coil located on a moving platform and coinciding with the axis of the measuring coil; a drive with a belt drive mounted on a stand and moving the movable platform between the Helmholtz electric rings along the scale with divisions; a support coil mounted on a stand between the Helmholtz electric rings at the level of their axis and parallel to the measuring coil at a distance from the axis of the rings equal to their radius; EMF recorder; a phase difference meter, the first inputs of which are connected to the inputs of the EMF recorder, and the second inputs to the conclusions of the support coil.

This training device for demonstrating the second Maxwell equation allows you to remove the dependence of the bias current on the frequency and intensity of the electric field, to determine the dependence of the magnetic field on the distance to the axis of the Helmholtz electric rings. On it, using the measuring coil, the module of the magnetic field vector is determined, and the direction of the vector is determined using the measuring and supporting coils, as well as a phase difference meter. Thanks to this, a right-handed system between the vectors of the bias current density and magnetic field strength is demonstrated.

Using this device, it is impossible to measure the electric field generated by Helmholtz electric rings, and also to calculate the electric field energy between Helmholtz electric rings and compare it with the magnetic field energy. This device does not allow determining the flux of the electric field vector and its sign, as well as experimentally confirming the Gauss theorem for an alternating electric field created by Helmholtz electric rings.

The aim of the invention is to expand the functionality of the training device to demonstrate the second Maxwell equation. This goal is achieved by the fact that the following are introduced into it: toroidal coil; dial in degrees in degrees, fixed at the top of Helmholtz's electric rings and parallel to the stand; a rod located between the Helmholtz electric rings perpendicular to the stand and the lower end is rigidly fixed to the toroidal coil so that the outer diameter of the latter coincides with the rod, and the upper end of the rod is mounted movably in the center of the dial with degrees in degrees; rod rotation handle with an indicator of angular position, rigidly fixed to the upper end of the rod; a bipolar switch for two positions, in which the common contacts of the first and second poles are connected to the inputs of the EMF recorder, the contacts of the first position of the first and second poles are connected to the terminals of the measuring coil, and the contacts of the second position of the first and second poles are connected to the terminals of the toroidal coil.

Figure 1-7 presents drawings explaining the principle of operation of the proposed installation. In Fig.8 shows a General view of the proposed installation, and Fig.9 - its prototype.

The proposed installation for the study of the electromagnetic field of Helmholtz electric rings contains: 1 - Helmholtz electric rings; 2 - sound frequency generator; 3 - measuring coil; 4 - EMF recorder; 5 - stand; 6 - movable platform; 7 - scale with divisions; 8 - pointer position measuring coil; 9 - belt drive; 10 - phase difference meter; 11 - supporting coil; 12 - toroidal coil; 13 - a dial with divisions in degrees; 14 - stock; 15 - rod rotation handle with an indicator of the angular position; 16 - bipolar switch into two positions.

Maxwell argued that any alternating electric field excites an alternating magnetic field in the surrounding space. To establish a connection between them, we consider the Helmholtz electric rings. In this case, between them there is a region of a practically uniform electric field (Fig. 1).

In the future, we will characterize the alternating electric field and the associated alternating magnetic field with the corresponding effective values of the electric field strength E, electric displacement D and magnetic field N.

The magnitude of the magnetic field depends on the distance r to the axis of the Helmholtz rings ab (Fig. 1). We define this dependence for the field inside the Helmholtz rings using the second Maxwell equation

$${\displaystyle \underset{L}{\oint }\overrightarrow{H}\overrightarrow{d}l={\displaystyle \underset{S}{\int }\frac{\partial \overrightarrow{D}}{\partial t}d\overrightarrow{S}}.\left(\mathrm{one}\right)}$$

по замкнутому контуру LTransform the left side of the expression (1). Choose as a closed loop L (figure 2) the line of force of the vortex magnetic field of the Helmholtz rings r <R, where R is the distance shown in figure 1. From figure 2 it is seen that the magnetic field strength is the same at all points equidistant from the axis of the Helmholtz rings, and is directed along the tangent to a circle with a radius r. Then the circulation of the vector $$\overrightarrow{H}$$

closed loop L

$${\displaystyle \underset{L}{\oint }\overrightarrow{H}\overrightarrow{d}l=H2\pi r=I_{\mathrm{from}m}.\left(2\right)}$$

всюду имеет однородное распределение, поэтому правую часть выражения (1) можно преобразовать следующим образом:Between Helmholtz rings, the electric field is homogeneous and the vector $$\frac{\partial \overrightarrow{D}}{\partial t}$$

everywhere has a uniform distribution, therefore, the right-hand side of expression (1) can be transformed as follows:

$${\displaystyle \underset{S}{\int }\frac{\partial \overrightarrow{D}}{\partial t}d\overrightarrow{S}=\frac{\partial D}{\partial \mathrm{<figure-callout\; id="2"\; label="t\; \pi \; r"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">t\; </figure-callout>}}\pi r^{}{}^2.\left(3\right)}$$

Given that the electric field between the Helmholtz rings varies according to the harmonic law E (t) = E _m sin2πνt, as well as the relation D = ε ₀ E, where ε ₀ is the electric constant, expression (3) can be written in another form:

$$i_{\mathrm{from}m}(t)={\displaystyle \underset{S}{\int }\frac{\partial \overrightarrow{D}}{\partial t}d\overrightarrow{S}=2{\pi }^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\nu {\epsilon }_0{E}_m\cdot \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">cos</figure-callout>}2\pi \nu t=I_{m_{\mathrm{from}\mathrm{<figure-callout\; id="2"\; label="m\; cos"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">m\; </figure-callout>}}}\cos 2\pi \nu t,\left(\mathrm{four}\right)}$$

- амплитуда тока смещения.where i _cm (t) is the instantaneous value, and $$I_{m_{\mathrm{from}m}}$$

- the amplitude of the bias current.

Accordingly, the effective value of the bias current “current” between the Helmholtz rings along the axis ab (Fig. 1) inside the cylinder with the base πr ²

$$I_{m_{\mathrm{from}m}}=2{\pi }^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\nu {\epsilon }_{0}E.\left(5\right)$$

Then the bias current, "current" inside the cylinder with the base πR ²

$$I_{m_{\mathrm{from}m}}=2{\pi }^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\nu {\epsilon }_{0}E.\left(6\right)$$

From equalities (2) and (5) we obtain the expression for determining the magnetic field strength between Helmholtz rings at a distance r from their axis:

$$H=\pi r\nu {\epsilon }_{0}E.\left(7\right)$$

Expression (7) shows that inside the Helmholtz rings (r <R), the magnetic field strength H increases with distance from their axis according to a linear law (Fig. 3).

Let us find the dependence of the magnetic field strength H on the distance to its axis outside the Helmholtz rings when r≥R. We choose point B (figure 2) outside the Helmholtz rings at a distance r from their axis, then the circulation of the vector H along the contour L is equal to the bias current "current" between the Helmholtz rings along the axis ab (figure 1) inside the cylinder with the base πR ² . From equalities (2) and (6) we obtain

$$H=\frac{\mathrm{<figure-callout\; id="2"\; label="\pi \; R"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\pi \; </figure-callout>}{R}^{}{}^2\nu {\epsilon }_{0}E}{r}.\left(8\right)$$

From the expression (8) it can be seen that the magnetic field strength H outside the Helmholtz electric rings varies inversely with the distance to their axis (Fig. 3). The magnetic field strength inside the Helmholtz electric rings (r <R) is determined by the "current" between the Helmholtz rings, the bias current inside the cylinder with the base πr ² . Find the relationship between the bias current I _cm and the magnetic field N. For this, we exclude E from the expressions (6) and (7), then we have:

$$I_{\mathrm{from}m}=\frac{2\pi R^2}{r}H.\left(9\right)$$

(фиг.2). В этом случае напряженность магнитного поля будет определяться по следующему выражению:From the expression (9) it is seen that to calculate the bias current, it is necessary to measure the value of H between the Helmholtz rings. To do this, in the studied point A (Fig.2) we place a measuring coil containing w turns and having such small dimensions that the field in its vicinity can be considered homogeneous. We position the measuring coil so that its axis coincides with the direction of the vector $$\overrightarrow{H}$$

(figure 2). In this case, the magnetic field strength will be determined by the following expression:

$$H=\frac{\mathrm{<figure-callout\; id="2"\; label="\epsilon \; w"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\epsilon \; </figure-callout>}}{w},\left(10\right)$$

where ε is the EMF induced in the measuring coil, ν is the frequency of the alternating magnetic field, μ ₀ is the magnetic constant, μ is the magnetic permeability of the core of the measuring coil, S is the cross-sectional area of the measuring coil.

Substituting expression (10) into (9), we find the dependence of the bias current on the emf measured by the recorder

$$H=\frac{{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">R</figure-callout>}}^2\epsilon }{r\mathrm{<figure-callout\; id="0"\; label="w\; \nu \; \mu "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">w\; </figure-callout>}\nu {\mu }_{}{}_0\mu S}.\left(\mathrm{eleven}\right)$$

To determine the bias current and construct the dependence of the magnetic field strength by formulas (5) - (8), as well as calculate other characteristics of the electromagnetic field under study, it is necessary to know the magnitude of the electric field E between Helmholtz electric rings. For these purposes, we use a toroidal coil containing w turns connected to an EMF recorder. In this case

$$E=\frac{\epsilon }{2\mathrm{<figure-callout\; id="2"\; label="w\; \pi "\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">w\; </figure-callout>}{\pi }^{}{}^2{\mathrm{<figure-callout\; id="2"\; label="\nu "\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\nu </figure-callout>}}^2{\mathrm{<figure-callout\; id="0"\; label="\epsilon "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_0\mathrm{<figure-callout\; id="0"\; label="\epsilon \; \mu "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\epsilon \; </figure-callout>}{\mu }_{}{}_0\mu R_B^{2}h\ln \frac{R_H}{R_B}},E=\beta \epsilon ,\left(12\right)$$

where ε is the EMF measured by the recording device, ν is the frequency of the alternating electric field, ε ₀ is the electric constant, ε is the dielectric constant of the medium between Helmholtz electric rings, μ is the magnetic permeability of the core of the toroidal coil, h is the axial size of the core, R _H and R _B is the outer and inner radii of the core, β is the coefficient of proportionality, depending on the frequency ν and the parameters of the toroidal coil.

For experimental verification of the Gauss theorem for an alternating electric field using Helmholtz electric rings, it is necessary to know the flux of intensity of a uniform electric field E through surface S (Fig. 6). It is determined by the following formula:

$$F_e=ES\cos \alpha =E_{n}S,\left(13\right)$$

на направление нормали $$\overrightarrow{n}$$

к поверхности S, определяемой наружным радиусом R_H тороидальной катушки; α - угол между векторами $$\overrightarrow{E}$$

и $$\overrightarrow{n}$$

. Знак потока напряженности электрического поля Ф_e зависит от угла α, как показано на фиг.5. Определение знака Ф_e можно осуществить с помощью измерителя разности фаз, где сравниваются фазы ЭДС тороидальной и опорной катушек. По знаку напряжения на выходе измерителя разности фаз определяется знак проекции Е_n и, соответственно, знак потока напряженности электрического поля Ф_e.where E _n is the projection of the vector $$\overrightarrow{E}$$

to the normal direction $$\overrightarrow{n}$$

to a surface S defined by the outer radius R _{H of the} toroidal coil; α is the angle between the vectors $$\overrightarrow{E}$$

and $$\overrightarrow{n}$$

. The sign of the flux of the electric field Φ _e depends on the angle α, as shown in FIG. The determination of the sign Ф _e can be carried out using a phase difference meter, where the phases of the EMF of the toroidal and reference coils are compared. The sign of the voltage at the output of the phase difference meter determines the sign of the projection E _n and, accordingly, the sign of the flux of the electric field Φ _e .

If the toroidal coil is placed in a uniform electric field of Helmholtz electric rings, as shown in Fig. 7, and the toroidal coil is represented as a closed surface S in the form of the sum S = S1 + S2 + S3 + S4, then the flow of tension through the closed surface S in accordance with the Gauss theorem will be:

$${\displaystyle \underset{S}{\oint }{E}_{n}dS={\displaystyle \underset{S\mathrm{one}}{\int }{E}_{n}dS+}{\displaystyle \underset{S2}{\int }{E}_{n}dS+{\displaystyle \underset{S3}{\int }{E}_{n}dS+{\displaystyle \underset{S\mathrm{four}}{\int }{E}_{n}dS=0.\left(\mathrm{fourteen}\right)}}}}$$

This is because the flows of tension through the surface S3 and S4 “slide” and equal to 0, and the flows through the surface S1 and S2 are equal in magnitude and opposite in sign. This can be seen from figure 5, where at α = 0 ° flux f_{e max}> 0, and for α=180 ° stream f_emax<0 and they are equal in magnitude. Figure 5 also shows that the toroidal coil can be used to determine the direction of the electric field by the minimum or maximum EMF in the toroidal coil, which corresponds to the minimum or maximum of_e.

From the measured electric field strength E using a toroidal coil, it is possible to calculate the volume density of electric energy between Helmholtz electric rings by the formula:

$$w_e=\frac{{\mathrm{<figure-callout\; id="0"\; label="\epsilon "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_0\mathrm{<figure-callout\; id="2"\; label="\epsilon \; E"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\epsilon \; </figure-callout>}{E}^{}{}^2}{2},\left(\mathrm{fifteen}\right)$$

as well as the maximum electrical energy concentrated between the Helmholtz electric rings, according to the formula:

$$W_e={\mathrm{<figure-callout\; id="0"\; label="\epsilon "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\epsilon </figure-callout>}}_0\mathrm{<figure-callout\; id="2"\; label="\epsilon \; E"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\epsilon \; </figure-callout>}{E}^{}{}^2\pi R^3\left(16\right)$$

and the maximum magnetic energy concentrated between the Helmholtz electric rings, according to the formula:

$$W_m=0.5{\mathrm{<figure-callout\; id="0"\; label="\mu "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\mu </figure-callout>}}_0\mathrm{<figure-callout\; id="0"\; label="\mu \; \epsilon "\; filenames="00000045.png,00000046.png"\; state="\{\{state\}\}">\mu \; </figure-callout>}{\epsilon }_{}^{}{}_0^2{\epsilon }^2{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">E</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="\nu "\; filenames="00000043.png,00000044.png"\; state="\{\{state\}\}">\nu </figure-callout>}}^2{\pi }^3{R}^5.\left(17\right)$$

Consider the operation of the proposed device (Fig.8). It contains Helmholtz electrical rings 1, located opposite and parallel to each other. Between them there is a region of almost uniform alternating electric field. This field is obtained by adding the vortex electric fields from both rings. The windings of the Helmholtz electric rings 1 connected to the sound frequency generator 2 create magnetic fields inside them, and they, in turn, create vortex electric fields.

According to Maxwell, an alternating electric field generates an alternating magnetic field around itself, the intensity of which can be determined by formula (10). To do this, we place the measuring coil 3 at the required point of the magnetic field, in which the EMF ε is proportional to H. We position the measuring coil so that its axis coincides with the direction of the magnetic field vector. EMF measurements are carried out by the EMF 4 recorder, for example, a voltmeter with a large input resistance.

To determine the dependence of the magnetic field strength H on the distance r from the axis of the Helmholtz electric rings 1, we move the measuring coil 3 between them along the stand 5, for this we place the measuring coil 3 on a movable platform 6. We place the measuring coil 3 on a movable platform 6 so that it was at the level of the axis of the Helmholtz electric rings 1 and at an equal distance from them. To count the distance from the axis of the Helmholtz electric rings to the measuring coil 3, a scale with divisions 7 is placed on the stand 5, and the movable platform 6 is provided with a pointer 8 of the position of the measuring coil coinciding with the axis of the measuring coil 3. The movable platform 6 is moved along the scale with divisions 7 using a belt drive 9 mounted on a stand 5.

Thus, according to the measured EMF in the measuring coil 3, it is possible to calculate by the formula (10) the magnetic field strength between the Helmholtz 1 electric rings at an arbitrary point. By the formula (11), it is also possible to calculate the bias current I _cm inside the Helmholtz electric rings 1.

The proposed installation allows you to remove the dependence of the bias current I _cm from the frequency ν and the magnitude of the electric field E. In addition, it allows you to familiarize yourself with the induction method of measuring the intensity of an alternating magnetic field created by the bias current between Helmholtz electrical rings 1.

не определяется. В действительности левая ветвь зависимости (фиг.3) имеет вид, показанной пунктирной линией. Для определения направления вектора $$\overrightarrow{H}$$

в исследуемой точке электромагнитного поля в предлагаемую установку (фиг.8) введен измеритель разности фаз 10. В нем сравнивается ЭДС, снимаемая с измерительной катушки 3 с ЭДС, снимаемой с опорной катушки 11. Опорная катушка 11 по конструкции аналогична измерительной катушке 3 и располагается на подставке между электрическими кольцами Гельмгольца 1 на уровне их оси, параллельно оси измерительной катушки 3. Опорная катушка 11 находится на расстоянии от оси электрических колец Гельмгольца 1, равном их радиусу.Using the measuring coil 3, the dependence of H on r, shown in Fig. 3 by a solid line, i.e. the modulus of the magnetic field H is removed, and the direction of the vector $$\overrightarrow{H}$$

not determined. In fact, the left branch of the dependency (Fig. 3) has the form shown by a dashed line. To determine the direction of the vector $$\overrightarrow{H}$$

at the studied point of the electromagnetic field, a phase difference meter 10 is introduced into the proposed installation (Fig. 8). It compares the EMF taken from the measuring coil 3 with the EMF taken from the supporting coil 11. The supporting coil 11 is similar in design to the measuring coil 3 and is located on the stand between the Helmholtz electric rings 1 at the level of their axis, parallel to the axis of the measuring coil 3. The support coil 11 is located at a distance from the axis of the Helmholtz electric rings 1, equal to their radius.

To measure the electric field E generated by Helmholtz electric rings 1, to determine the flux of vector E through a given surface and its sign, as well as to experimentally confirm the Gauss theorem for an alternating electric field between Helmholtz electric rings 1, the proposed device contains: toroidal coils 12, dial with divisions in degrees 13, rod 14, rod rotation handle with an indicator of angular position 15 and a bipolar switch for two positions 16.

A dial with degrees in 13 is fixed at the top of the Helmholtz electric rings 1 and is parallel to the stand 5. The rod 14 is perpendicular to the stand between the Helmholtz electric rings 1. The lower end is rigidly fixed to the toroidal coil 12 so that the outer diameter of the latter coincides with the rod 14. The upper end of the rod 14 is mounted movably in the center of the dial with graduations in degrees 13. At the upper end of the rod 14 there is a rod rotation handle with an indicator of the angular position 15, which provides rotation of the toroidal coil 12 from 0 to 360 degrees and determination of the angle of rotation on a dial with a division in degrees 13. The introduced bipolar switch into two positions 16 provides the connection of either measuring coil 3 (first position "IR"), or toroidal coil 12 (second position "TC") to the inputs of the EMF 4 recorder and the first inputs of the phase difference meter 10.

Consider the operation of the proposed installation in the first position "IR" of the bipolar switch into two positions 16. In this case, through the contacts of the first position of the first and second poles, the measuring coil 3 is connected to the inputs of the EMF recorder 4 and the first inputs of the phase difference meter 10. To the first input of the difference meter phase 10 fed EMF, removed from the measuring coil 3, and at its second input fed EMF, removed from the reference coil 11.

Phase difference meters are described in (Kushnir V.F. et al. Measurements in communication technology. M: Communication, 1970, p. 318). For example, if we use a phase detector as a phase difference meter 10, then its detector characteristic is shown in Fig. 4, showing the dependence of the output voltage on the phase difference φ.

на направление нормали $$\overrightarrow{n}$$

к измерительной катушке 3 (фиг.3).Suppose that in the initial position the movable measuring coil 3 and the stationary support coil 11 are located nearby at a distance R equal to the radius of the Helmholtz electric rings 1. The terminals of the support coil 11 should be connected to the second input of the phase difference meter 10 so that the output of the phase difference meter 10 positive voltage (figure 4). This indicates a zero phase shift φ between the measured and reference EMF. In this case, the positive voltage at the output of the phase difference meter 10 corresponds to the positive projection of the vector $$\overrightarrow{H}$$

to the normal direction $$\overrightarrow{n}$$

to the measuring coil 3 (figure 3).

на направление нормали $$\overrightarrow{n}$$

к измерительной катушке 3 (фиг.3). Зависимость H от r влево от точки r=0 показана пунктирной линией на фиг.3.If the measuring coil 3 is displaced to the left relative to the stationary support coil 11, then we will observe a decrease in the EMF taken from the measuring coil 3, and in accordance with formula (10), the stress modulus H will decrease (Fig. 3). Passing the point of the center of Helmholtz electric rings 1 (r = 0), we observe a jump in the phase difference φ between the measured and reference EMF by π. The phase difference meter will indicate a negative voltage. This indicates a negative projection of the vector $$\overrightarrow{H}$$

to the normal direction $$\overrightarrow{n}$$

to the measuring coil 3 (figure 3). The dependence of H on r to the left of the point r = 0 is shown by the dashed line in Fig. 3.

(фиг.3).Thus, in the proposed installation, according to the EMF readings taken from the measuring coil 3, we calculate by the formula (10) the magnetic field strength module, and from the voltage sign at the output of the phase difference meter 10, we determine the direction of the vector $$\overrightarrow{H}$$

(figure 3).

и вектором напряженности магнитного поля $$\overrightarrow{H}$$

. На фиг.1 показаны направления этих векторов для случая, когда $$\frac{\partial \overrightarrow{D}}{\partial t}>0$$

, а также направление вектора Пойтинга $$\overrightarrow{S}$$

.According to the readings of the phase difference meter 10, it is possible to demonstrate a right-handed system between the bias current density vector $${\overrightarrow{j}}_{\mathrm{from}m}$$

and the magnetic field vector $$\overrightarrow{H}$$

. Figure 1 shows the directions of these vectors for the case when $$\frac{\partial \overrightarrow{D}}{\partial t}>0$$

, as well as the direction of the Poiting vector $$\overrightarrow{S}$$

.

Consider the operation of the proposed installation in the second position of the "TC" of the bipolar switch to two positions 16. In this case, through the contacts of the second position of the first and second poles, a toroidal coil 12 is connected to the inputs of the EMF 4 and the first input of the phase difference meter 10. To the first input of the difference meter phase 10 is fed EMF, removed from the toroidal coil 12, and the second input is fed EMF, removed from the reference coil 11.

на направление $$\overrightarrow{n}$$

к тороидальной катушке 12 (фиг.6).Let in the initial position, the stationary support coil 11 is located on the stand 5 at a distance equal to the radius of the Helmholtz electric rings. We install the toroidal coil 12 using the rod rotation handle with the indicator of the angular position 15 parallel to the Helmholtz electric rings 1, in this case the indicator of the angular position will show 0 degrees on a dial with a division in degrees 13. The conclusions of the toroidal coil 12 should be connected to the first inputs of the difference meter phases 10 so that at the output of the meter of the phase difference 10 there was a positive voltage (figure 4). This indicates a zero phase shift between the measured and reference EMF. In this case, the positive voltage of the phase difference meter 10 is taken as the positive projection of the vector $$\overrightarrow{E}$$

to direction $$\overrightarrow{n}$$

to the toroidal coil 12 (Fig.6).

на направление нормали $$\overrightarrow{n}$$

к тороидальной катушке 12 (фиг.6). Полная зависимость Ф_e от угла α между векторами $$\overrightarrow{E}$$

и $$\overrightarrow{n}$$

показана на фиг.5.If the toroidal coil 12 is rotated clockwise from 0 to 360 degrees, then we will observe a change in the EMF taken from the toroidal coil 12, and in accordance with formula (12), the modulus of tension E will change. Passing an angle of 90 degrees on a scale divided by 13 degrees, a jump in the phase difference between the measured and reference EMF by π will be observed. A phase difference meter 10 will indicate a negative voltage. This indicates a negative projection of the vector $$\overrightarrow{E}$$

to the normal direction $$\overrightarrow{n}$$

to the toroidal coil 12 (Fig.6). The full dependence of Ф _e on the angle α between the vectors $$\overrightarrow{E}$$

and $$\overrightarrow{n}$$

shown in figure 5.

Thus, in the proposed installation, according to the EMF readings taken from the toroidal coil 12, we calculate the projection module E _n using formula (12), and determine the projection sign E _{n from the} voltage sign at the output of the phase difference meter 10. By the formula (13), we calculate the flux of the electric field Φ _e . From the graph (Fig. 5), we take the quantities Ф _{е max} and -Ф _{е max} and make sure that the total flux of the electric field vector through the surface S in accordance with the Gauss theorem (14):

. $${\displaystyle \underset{S}{\oint }{E}_{n}dS=}{F}_{e\max }-F_{e\max }=0$$

.

To determine the volume density of electric energy w _e by the formula (15), the maximum electric and magnetic energy, respectively, by the formulas (16), (17), we take the effective value of the electric field strength E, which is determined by the formula (12). When measuring E, the toroidal coil 12 is set with the help of a rod rotation handle with an indicator of the angular position of 15 by 0 degrees on a dial with divisions in degrees 13.

The technical and economic efficiency of the proposed installation for the study of the electromagnetic field of Helmholtz electric rings lies in the fact that it provides an increase in the quality of assimilation by cadets of the basic laws and phenomena of physics.

The proposed installation is implemented at the Department of Physics A.F. Mozhaiskogo and is used in the educational process in laboratory studies on magnetism.

Claims (1)

An installation for studying the electromagnetic field of Helmholtz electric rings, containing Helmholtz electric rings mounted perpendicularly to the stand, and the leads of which windings are connected to the output terminals of the sound frequency generator, a movable platform moving along the stand between the Helmholtz electric rings along the scale with divisions, a measuring coil installed on a moving platform at the level of the axis of the Helmholtz electric rings and an equal distance from them so that the measuring axis the coil was perpendicular to the stand, the position indicator of the measuring coil located on the movable platform and coinciding with the axis of the measuring coil, the belt drive mounted on the stand and moving the moving platform between the Helmholtz electric rings along the divisions scale, the support coil mounted on the stand between the electric Helmholtz rings at the level of their axis and parallel to the measuring coil at a distance from the axis of the Helmholtz electric rings equal to their radius EMF emitter, phase difference meter, the first inputs of which are connected to the inputs of the EMF recorder, and the second inputs to the outputs of the support coil, characterized in that a toroidal coil, a circular scale with degrees in degrees, fixed at the top of the Helmholtz electric rings and located parallel to the stand, the rod located between the Helmholtz electric rings perpendicular to the stand and the lower end is rigidly fixed to the toroidal coil so that the outer diameter of the latter coincides with the piece com, and the upper end of the rod is mounted movably in the center of the dial with graduations in degrees, the rod rotation handle with an indicator of the angular position, rigidly fixed to the upper end of the rod, a two-pole switch for two positions, in which the common contacts of the first and second poles are connected to the inputs of the recorder EMF, the contacts of the first position of the first and second poles are connected to the terminals of the measuring coil, and the contacts of the second position of the first and second poles are connected to the terminals of the toroidal coil.

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