Training device for demonstration of second maxwell equation

FIELD: training devices, possible use in laboratory practicum on physics for studying physical rules and occurrences.

SUBSTANCE: device contains two even toroids, positioned oppositely and in parallel to one another at distance of their radius. Outputs of windings of toroids are connected to output clamps of sound frequency generator. Both toroids are mounted on substrate, on which scale with points is installed. Moveable platform is positioned on substrate between toroids along the scale with points. Measuring coil is mounted on moveable platform at the level of axis of toroids and at even distance from them so, that its axis coincides with direction of strength vector of magnetic field, created by electric field of toroids. Position pointer of measuring coil is positioned on moveable platform and coincides with axis of measuring coil. Input clamps of EMF registrar are connected to outputs of measuring coil. Drive with belt transmission is held on substrate and is used for moving moveable platform between aforementioned toroids along the scale with points for counting distance from axis of toroids to measuring coil with position pointer. Supporting coil is mounted on the substrate between toroids at the level of their axis and in parallel to measuring coil at distance from axis of toroids, equal to their radius. Device contains device for measuring phase difference, first input of which is connected to outputs of measuring coil, and second output - to outputs of supporting coil. Device allows measuring dependence of shift current from frequency and strength of electric field. On basis of indications of phase difference meter it is possible to demonstrate right-handed screw system between vectors of shift current density and magnetic field strength.

EFFECT: expanded research area, increased precision of measurements.

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The invention relates to educational devices and can be used in the laboratory in higher and secondary special educational institutions on physics course for exploring and deepening the knowledge of physical laws and phenomena.

Known training device physics (RU patent No. 2133505, 20.07.99, bull. No. 20), containing a solenoid connected to the generator of the harmonic voltage. It allows you to demonstrate the first Maxwell equation, showing that the alternating magnetic field generates around itself an alternating electric field. It is impossible to demonstrate the second Maxwell equation, showing that alternating electric field generates around itself an alternating magnetic field.

Also known training device physics to demonstrate the Maxwell equations (RU patent No. 2130204, 10.05.99, bull. No. 13), containing capacitor plates connected to a source of alternating voltage. This device allows you to demonstrate the second Maxwell equation, measuring the magnitude of the magnetic field strength between the plates of the capacitor. It is difficult to obtain exact dependence of magnetic field strength on the distance from the center of the capacitor plates.

Closest to the proposed educational device for demonstrating the second of Maxwell's equations is a training device for the study of electromagnetic who itogo field (RU patent No. 2210815, G 09 B 23/18, 20.08.2003, bull. No. 23, Author: Kownacki VK). The device contains two equal toroid located opposite and parallel to each other on the distance of their radius. Conclusions winding toroids are connected with output terminals of the generator audio frequency. Both toroid is placed on the stand on which the graduated scale. The mobile platform moves to stand between the toroids along the scale with tick marks. The measuring coil is installed on a movable platform at the level of the axis of the toroids and equal distance from them so that its axis coincides with the direction vector of the magnetic field created by the electric field of toroids. The positioner of the measuring coil is mounted on a platform and coincides with the axis of the measuring coil. Input terminals of the Registrar EMF is connected with the conclusions of the measuring coil. Drive belt driven mounted on the stand and moves the movable platform between these toroids along the scale with tick marks to count down the distance from the axis of the toroids to the measuring coil with a position indicator.

The device allows you to remove the dependence of the bias current from the frequency and the intensity of the electric field to determine the dependence of magnetic field strength on the distance from the axis of the toroids. This instrument measured only the module of the vector e.g. the debts of the magnetic field, and the direction of the vector depending on the distance to the axis of the toroids are impossible to determine. It is impossible to demonstrate bravofineboy system between vectors density of the bias current and the magnetic field.

The aim of the invention is to enhance the functionality of this device.

This goal is achieved by the fact that it introduced the reference coil, mounted on the stand between the toroids on the level of their axis and parallel to the measuring coil at a distance from the axis of the toroids, equal to their radius, measuring the phase difference, the first input connected with the conclusions of the measuring coil and the second input it is connected with the conclusions of the reference coil.

In figure 1, 2, 3, and 4 are drawings explaining the operation principle of the proposed training device. Figure 5 shows a General view of the proposed device, and figure 6 is a prototype.

The proposed device contains 1 - toroids; 2 - generator audio frequency; 3 - measuring coil; 4 - Registrar EMF; 5 - stand; 6 - movable platform; 7 - scale with divisions; 8 - pointer of the provisions of the measuring coil; 9 - motor with belt transmission; 10 - meter phase difference; 11 - supporting coil.

Maxwell argued that any alternating electric field excites the surrounding space alternating magnetic field. To link edit the available electric field, the underlying magnetic field, consider two equal toroid located parallel to each other on one axis of the toroids. In this case, between them there is a region of almost uniform electric field (figure 1).

In the future will be characterized by an alternating electric field and an associated alternating magnetic field corresponding to the current values of the electric field E, the electric displacement D and magnetic field strength H.

The magnitude of the magnetic field H depends on the distance r to the axis of the toroids ab (figure 1). Determine this dependence for the field inside the toroids (r<R), it will use the second equation of Maxwell

Convert the left side of the expression (1). Let us choose as a closed path L (2) power line vortex magnetic field inside the toroids 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 toroids, and is directed along the tangent to the circle of radius r. Then the circulation of the vectorin the closed loop L

Between the toroids homogeneous electric field and the vectoreverywhere has a uniform distribution, is therefore the right part of the expression (1) can be converted as follows:

Given that the electric field between the toroids changing harmonic lawand the relationship D=ε₀E, where ε₀- electric constant, the expression (3) can be written in another form:

where i_cm(t) is the instantaneous value, andthe amplitude of the bias current.

Accordingly, the effective value of the bias current, "current" between the toroids along the axis ab (Fig 1) inside a cylinder with base πr²,

Then the displacement current, "current" inside a cylinder with base πR²,

From the equality (2) and (5) we obtain the expression for determining the magnetic field strength between the toroids on the distance r from the axis

Expression (7) shows that inside the toroids (r<R) the intensity H of the magnetic field increases with distance from the axis of the toroids is linear (figure 3).

Find the dependence of the intensity H of the magnetic field on the distance from its axis outside the toroids, when r≥R. Select a point In the (2) outside the toroids on the distance r from the axis, then the circulation of the vectorthe contour L is equal to the bias current, "current" between the toroids along about who and ab (figure 1) inside the cylinder with base π R². From the equality (2) and (6), we obtain

From the expression (8) shows that the intensity H of the magnetic field outside the toroids depends inversely on the distance r to the axis (figure 3). The magnetic field strength inside the toroids (r<R) is determined by the "current" between the toroids bias current inside a cylinder with base πr².

Find the relationship between the bias current I_cmand the magnetic field H. This will exclude from the expressions (6) and (7) E, then we have:

From the expression (9) shows that for the calculation of the bias current it is necessary to measure the value of N between the toroids. To measure N in the test point And (2) place the measuring coil containing w coils and having such small dimensions that the field in its surroundings can be considered homogeneous. The measuring coil is disposable so that its axis coincides with the direction of the vector(figure 2). In this case, the magnetic flux f, penetrating the measuring coil will be proportional to N and defined by the following expression:

where μ₀- magnetic constant, μ - the magnetic permeability of the coil core, S is the cross-sectional area of the measuring coil. From the last expression

As the bias current (4) is changed according to the harmonic law, and the magnetic flux through the measuring coil will also change by the same lawand in a single turn coil will be picking up EMF

where- the amplitude of the EMF.

Accordingly, the value of the RMS EMF

From expressions (10) and (11), we obtain

Substituting the expression (12) in (9), we find the dependence of the bias current I_cmfrom the measured Registrar EMF

Consider the work of the proposed instrument (figure 5). It contains two equal toroid 1, located opposite and parallel to each other. Between them there is a region of almost uniform AC electric field. This field is obtained by adding the vortex electric fields from both toroids 1. Toroids winding coils are connected to the sound generator frequency 2 create inside a magnetic field, and they, in turn, creates a vortex electric field.

According to Maxwell alternating electric field generates around itself an alternating magnetic field, the intensity of which can be defined by the formula (12). For ecogov desired point of the magnetic field put the measuring coil 3, in which the induced EMF εthat is proportional to N. The measuring coil is disposable so that its axis coincides with the direction of the magnetic field intensity vector. Measurement of EMF carried out by the Registrar EMF 4, for example a voltmeter with high input resistance.

To determine the dependence of the intensity H of the magnetic field on the distance r to the axis of the toroids measuring coil 3 move between the toroids 1 along the stand 5, for measuring the coil 3 is placed on a movable platform 6. The measuring coil 3 located on the movable platform 6 so that it was at the level of the axis of the toroids 1 and equidistant from them. For reference, the distance from the axis of the toroids to the measuring coil 3 on the cradle 5 is placed a scale with divisions 7 and the movable platform 6 is provided with a pointer 8 position measuring coil coinciding with the axis of the measuring coil 3.

The graduated scale 7 for counting the distance from the center of the toroids 1 is placed on the cradle 5, in which the movable platform 6 is moved between the toroids 1 along a scale with divisions 7 with a drive belt transmission 9, mounted on the cradle 5.

Thus, the measured voltage in the measuring coil 3 can be calculated by the formula (12) the magnetic field strength between the toroids in arbitrary is the point. By the formula (13) can also calculate the bias current I_cminside the toroids.

The proposed device allows you to remove the dependence of the bias current I_cmfrequency ν and the magnitude of the intensity E of the electric field. In addition, it allows you to familiarize yourself with the induction method of measuring the intensity of the alternating magnetic field created by the bias current I_cmbetween the toroids.

In a known device (6) is removed dependence n of r, shown in figure 3 by the solid line, i.e. removed the module intensity H of the magnetic field and the direction of the vectoris not defined. In fact, the left branch of the dependence (figure 3) has the form shown in dotted lines. To determine the direction of the vectorin the point of the electromagnetic field of the proposed device (6) is measuring the phase difference 10. It compares the EMF produced by the measuring coil 3, with reference EMF. For this purpose, in the known device entered the reference coil 11, which by design is similar to the measuring coil 3 and is located on a stand between the toroids on the level of their axis parallel to the axis of the measuring coil 3. The reference coil 11 is located at a distance from the axis of the toroids, equal to their radius. On the first entrance of measuring the phase difference of 10 served EMF, with imama with the measuring coil 3, and at its second input EMF removed from the reference coil 11.

Measuring the phase difference described in (F. W. Kushnir and other Measurements in communications technology. M: Communications, 1970, s). For example, if measuring the phase difference of 10 use a phase detector, figure 4 shows its rectifying characteristic, showing the dependence of the output voltage from the phase difference ϕ.

Let the initial position of the movable measuring coil 3 and the fixed reference coil 11 are adjacent at a distance R equal to the radius of the toroids. Conclusions measuring coil 3 should be connected to the first input of measuring the phase difference of 10 and the reference coil 11 are connected to the second input of the measuring phase difference 10 so that at the output of measuring the phase difference of 10 were positive voltage (figure 4). This indicates zero phase shift ϕ between the measured and reference EMF. In this case, a positive voltage is taken as positive projection vectorat the direction of the normalto the measuring coil 3 (Fig 3).

If the measuring coil 3 move to the left relative to the stationary support coil 11, then we will observe a decrease in EMF removed from the measuring coil 3, and in accordance with the formula (12) module tension N will decrease Atisa (figure 3). Passing through the center point of the toroids (r=0) we observe a jump in the phase difference (between the measured and reference EMF 180°. Measuring the phase difference will reflect a negative voltage. This indicates a negative projection vectorat the direction of the normalto the measuring coil 3 (Fig 3). Dependencefrom r to the left of point r=0 is shown by the dashed line in figure 3.

Thus, in the proposed device for EMF readings taken with the measuring coil 3, calculated according to the formula (12), the module of the magnetic field strength and the sign of the voltage at the output of measuring the phase difference of 10 defined by the direction of the vector(figure 3).

According to the testimony of measuring the phase difference of 10 you can demonstrate bravofineboy system between the vector current density offset

and the magnetic field intensity vector.

Figure 1 shows the directions of these vectors for the case when

Technical and economic efficiency of the proposed training device physics is that it provides improved quality of mastering the fundamental laws of physics students.

The proposed device is implemented in the Department who Iseki and used in the classroom laboratory exercises in electromagnetism.

Educational device for demonstrating the second Maxwell's equations containing two equal toroid located on the length of their radius opposite and parallel to each other and mounted on the stand, and the conclusions winding toroids are connected with output terminals of the generator audio frequency, a movable platform, moving to stand between the toroids along the scale with divisions, the measuring coil is mounted on a movable platform at the level of the axis of the toroids and equal distance from them so that the axis of the measuring coil coincides with the direction vector of the magnetic field created by the electric field of toroids, the pointer position measuring coil located on a movable platform and matching the axis of the measuring coil, the Registrar EMF, input terminals of which are connected with the conclusions of the measuring coil, the drive belt gear fixed on a stand and moving the movable platform between the toroids along the scale with tick marks to count down the distance from the axis of the toroids to the measuring coil with position indicator, characterized in that it introduced the reference coil, mounted on the stand between the toroids on the level of their axis and parallel to the measuring coil at a distance from the axis of the toroids, equal to their radius, measuring the phase difference, the first in the od which is connected with the conclusions of the measuring coil, and the second input with the conclusions of the reference coil.