The physics laboratory works - individualized computer simulations

The physics laboratory-works creating and operating computer simulations experience is described. A significant amount of laboratory works can be classified as a"black box". The studied physical phenomenon is hidden from direct observation, the control is carried out by means of electrical measuring devices. It is difficult to distinguish physical reality from its imitation when performing such work, so the virtualization of this one does not require realistic images. The schematic representation of the laboratory installation greatly simplifies the process of creating a simulator. A unique set of installation parameters is formed for each student performing laboratory work on the simulator. These parameters are stored in Google Tables. Their transfer to the laboratory works html-template is carried out in encrypted form through the Google Apps script service. The simulator-parameters individualization contributes to the independence of the student's work when performing laboratory measurements in the conditions of the distance learning.


Introduction
The development of distance education, having a rich history, has become avalanche-like in the last two years.The teaching community suddenly faced issues of a methodological, organizational and scientific nature that were previously unknown to most.
The specifics of higher school disciplines are such that the transition was almost painless for some of them, but for others it required a radical breakdown of the educational process, and some ones are simply impossible in a distance format.
The physics course for engineers involves various forms of interaction with the student.Apparently, it is most difficult to translate a laboratory workshop into a remote format, although virtual and remote laboratory work has been practiced before.Such developments were based on the enthusiasm and the availability of appropriate skills of the teacher.The pandemic has made this direction mandatory.
Laboratory practical training in physics is very important and instructive for the full-fledged understanding formation of the physical phenomena essence in a student.The laboratory work performed together with the study of theoretical material helps to feel the connection of a physical experiment with theoretical concepts, to understand and assimilate new knowledge more deeply.In 2 addition, the student gets the skill of working with devices, learns to measure and process measurement results, build dependencies and graphs.
Here is a brief overview of existing solutions in this area.
Laboratory work performed at home [1] is one of the ways to conduct remote classes.In such works, the student is supposed to use not specialized equipment, but devices that have a household purpose, for example, scales, a thermometer, 3D glasses, a laser pointer, a smartphone, etc.
Methodological recommendations for home laboratory work usually regulate only the main stages of their implementation.The student is given more freedom of action than working in a training laboratory.The studied physical phenomenon is real and tangible.
The project of an Internet laboratory with remote control for conducting experiments in physics is very interesting [2].The user, through a browser, gets access to a webcam and electronic components located in a remote laboratory, such as a USB K8055 board, an Arduino with an Ethernet Shield, a Raspberry Pi, to control a real physical device.The natural limitation of the project is the throughput capacity.Developers solve this problem, which occurs when working on any real laboratory installation, by booking access time.If the installation is free, then you can immediately start measuring.
Computer simulations imitate a physical phenomenon allowing you to visualize processes that are inaccessible to a direct observation, scale them in space and time.In classes, both lectures and seminars, simulators are used as animated illustrations.This form of presentation of the material is more effective than static drawings and can often compete with full-scale demonstrations.
Usually a computer simulation is a complete program created on the basis of a certain technology, it can be a Java applet or an Adobe Flash file.It should be noted that these technologies are outdated and are no longer supported by manufacturers.A demonstration of simulators implemented using these technologies on the user's device is a often difficult and sometimes unrealizable task.The HTML5 markup language is considered a modern tool, which allows you to run a simulation in modern browsers on any device.The PhET project [3], implemented by the University of Colorado, is one of the most wellknown and well-developed in this field and offers a wide range of interactive scientific and mathematical simulations.
A simulation model of a physical process is implemented in such a way that it often includes a more or less realistic image of measuring devices and other equipment.Such simulations can be adapted as a stand for laboratory work, exerting a certain amount of ingenuity [4].
system [5].Almost always, this operating system is the Windows OS family.The authors are not aware of cross-platform solutions for such products.The student installs the program after downloading it on the computer.The installation process is not always smooth.The reasons for the difficulties are very diverse: outdated and unsupported versions of the operating system, the presence of the required archiver and application libraries, the interaction of the program with antivirus protection, the lack of rights to install the software product.
As the most modern browsers adhere to international standards in the field of data processing and display, performing a laboratory work simulation directly in the browser allows you to use any device: a computer, tablet, smartphone.This approach seems to be optimal.
The Internet resource [6] contains more than two hundred virtual laboratory works and demonstrations in all sections of physics.However, for them to work, the Adobe Flash Player plugin, not currently supported, must be installed in the user's browser.These circumstances significantly limit the possibilities of using this product.The complexity of the launch may exceed the complexity of performing the laboratory work itself.

Proposed solutions
The experience of transferring the course of general physics of engineering specialties of the technical University to the remote format of a laboratory workshop follows below.
It is difficult to overestimate the visibility of some very simple physical experiments from the point of view of implementation.The phenomena arising from the free oscillations of coupled pendulums, the standing wave formation on a string, the laser light interference and diffraction, the light beam quenching by two transparent plates of polarizers border on magic.With the virtualization of such physical phenomena the loss of direct participation in the process is inevitable, despite all the power of modern technologies.
However within the framework of a standard laboratory practice in physics there is a significant number of works that can be classified as a "black box".As a rule these are ones related to electrical measurements.
An example of such work is the electron-specific-charge determination by the magnetron method, where the processes are monitored by means of measuring devices: a voltmeter and ammeters.
It is extremely difficult in fact to distinguish a physical reality from its imitation by registering the readings of instruments when performing this work.
In our opinion, the virtualization of such works does not require a naturalistic image of the devices, a conditional schematicity is quite enough, thus significantly simplifies the simulator development technology.In order to familiarize the student with real devices, if other options are unavailable, accompanying video clips will be suitable.
The independent performance of laboratory work by a student is a problem that has become relevant in the distance learning conditions.The parameters of the virtual laboratory installation controlled by the teacher and individual for each student are one of the possible answers to this challenge.
As the first step, five laboratory works that are in demand in the current educational process were selected from an extensive laboratory workshop for virtualization.Each of them corresponds to the definition of a "black box".A detailed description of the work is given below.
The creation of all simulators was carried out using a single technology developed for this task.
It is based on browser solutions using the HTML5 markup language, which simplifies the creation and management of multimedia objects without the need to use third-party plugins.
On the corresponding web page of the university portal [7] the student forms a request to perform a specific laboratory work.To do this, he fills in the fields determining the number of the study group, last name and password (Figure 1).The student who is allowed to perform the work receives the password from the teacher.Fig. 1 When the "Execute" button is clicked, a PHP script is launched that loads an HTML template of the laboratory work containing diagrams, drawings, control elements and PHP scripts that implement a mathematical model of the physical process under study.
The general elements of the template are supplemented with the student's personal data and the installation parameters individualized for him.This data is contained in a Google table that includes group lists of students and a logbook sheet in which the student's work is logged: login date, group, last name, IP address and browser.
The PHP template script gets access to the Google Table through the Google Apps Script, published as a web application.Google Apps Script is a development platform for creating small applications that integrate with Google Workspace.
Firstly the Google Apps script checks whether the entered personal data matches the data contained in the table.A mismatch leads to a denial of access.If this stage is successfully passed, a string of individual parameters is formed and returned in encrypted form to the template of the laboratory work.Some of the individualized installation parameters are hidden, inaccessible to observation during the execution of the work.They are determined by the student based on the processing measurements results.On the contrary, others are open.These ones can be the value of the capacitance, inductance, electromotive force, the maximum value of the current.These parameters are displayed on the screen, fall into the laboratory work report.They are individual therefore they allow the teacher to identify each student not only by the last name.
The cathedral workshop, which contains a significant number of real laboratory works on various branches of physics, is presented in [8].The principle of selecting works for virtualization, defined above, was combined with the requirements of the current educational process.Next, we will describe the features of the five developed simulators.

The direct multiple measurements processing
Laboratory practical training in physics usually begins with the exploration the direct-multiplemeasurements processing methods by the student.The ways of implementing a specific measurement procedure are very diverse.Measuring the spring pendulum oscillation period, the isotope source intensity, the ball diameter, the electric circuit parameters is only a small list of possible options.In the workshop [8] for these purposes the collision time of metal balls is measured with a microsecondometer.
We believe the use of computer simulation for carrying out such laboratory work is quite justified.
A sample of 50 numbers distributed according to the normal law is pre-generated for each student.The average value and the standard deviation are individual.
The methods of generation can be very different, for example, it can be carried out directly in the Google table.

6
We get the required number of values distributed according to the normal law by writing a formula in one of the cells and dragging the autofill marker.
You should not use the resulting sample blindly, without visualization.The sample of 50 values is not very representative, as a result the histogram does not always take canonical forms, losing its visibility.An example of an unsuccessful histogram is shown in Figure 2 on the left.For educational purposes, it is preferable to use the option shown on the right.An acceptable option is obtained by simply recalculating the entered formulas.Fig. 2 The template of this work contains a short video fragment of the two balls collision, as well as a control elementthe "Start" button, Figure 3.When the button is pressed, the video fragment is played, and the time of the collision is displayed on the stopwatch display.Fig. 3 The student's laboratory work consists in pressing the "Start" button fifty times and registering the microsecond meter readings in the measurement table.The subsequent processing of the measurement results is carried out in accordance with the requirements of the methodological recommendations.

Study of the Boltzmann distribution
The object of research in this work is an electrons cloud located between the cathode and the anode of an electric vacuum diode.The electrons emitted by the cathode form an ideal gas whose temperature is equal to the cathode's one.The concentration of the electron gas is constant in the absence of an electric field.In the presence of an external force field the concentration becomes spatially inhomogeneous.The reverse inclusion of the diode (a positive potential is applied to the cathode and a negative potential is applied to the anode) reduces the concentration of electrons from the cathode to the anode according to the Boltzmann distribution.
The computer simulation template along with the control elements contains a schematic diagram of the installation, Figure 4.The scheme includes an ammeter, a voltmeter measuring the voltage between the anode and the cathode, and a rheostat.The student, when performing this laboratory work, moves the slider of the rheostat, registers the readings of the ammeter and voltmeter, then constructs the current-voltage characteristic and calculates the temperature of the electron gas.

Study of the operation of a DC power source
An unbranched DC electrical circuit contains a current source and a resistor with variable resistance.The measuring instruments, ammeter and voltmeter are connected as shown in the diagram (Figure 6).The dependence of the voltage drop on the resistor on the current U E Ir  is linear.By measuring the current-voltage characteristic evaluation it is possible to determine the electromotive force (EMF) E of the source, its internal resistance r , short-circuit current sc I E r  , useful and full power.

The electron specific charge determination
The central element of a laboratory installation for measuring the electron specific charge is a magnetron, an electro-vacuum triode placed in a solenoid.The dependence of the anode current versus the solenoid one allows you to calculate the specific charge.The computer simulation template includes a schematic diagram of the installation and control elements, Figure 7.These include two ammeters, one in the solenoid circuit, another in the anode one, a voltmeter measuring the anodecathode voltage, and two rheostats.
The anode-cathode voltage is set using the rheostat R 1 .The rheostat R 2 regulates the current in the solenoid circuit from 0 to 2 A in increments of 1 mA.The anode current is measured by an ammeter A 1 , and the current in the solenoid circuit is measured by an ammeter A 2 .
The analysis of the motion of electrons in a magnetron leads to the following conclusion.The We will construct a correspondence between the anode-cathode voltage U and the cutoff current I С , as well as the anode current at zero current in the solenoid circuit I 0 .
To calculate the anode current, we use the three-halves-power law 32 0 where a is the perveance, a coefficient that depends on the configuration, dimensions and material of the electrodes.
The simulation parameters are selected so that the quantitative results of the experiments correspond to the operating modes of the real installation.If an interval 0.05 0.0995 a


is choosed 11 for the perveance, then at voltages (60-80) V the values of the anode current will be in the range (23-71) mA.
Let the number of turns of the solenoid be N, the length is l, and the radius is R, then these parameters and the electron specific charge are related by the ratio The correction factor K is introduced to account for the inhomogeneity of the magnetic field.
For the cut-off current of the ideal step we obtain отс I b U  , where Assuming the parameters of the magnetron as follows: and taking into account that  The open parameter in this work is the number of the magnetron turns N, and the closed parameter is the perveance a.
Performing the work, the student sets the anode voltage with the rheostat R 1 , moves the rheostat R 2 slider, registers readings of ammeters A 1 , A 2 , then builds the anode -solenoid currents dependence.

Forced oscillations in the oscillatory circuit
The voltage on the capacitor of an oscillatory circuit containing a series-connected harmonic signal generator depends on the signal frequency.The phenomenon of resonance can be studied by measuring the capacitor voltage dependence on frequency.The schematic diagram of the laboratory installation is shown in Figure 9. Fig. 9 13 In addition to the mentioned generator and voltmeter, measuring the voltage, the installation contains a rheostat.
The control elements of the simulation are a slider that changes the frequency of the generator output signal, and a slider rheostat that changes the resistance of the oscillatory circuit.
The following constants are individual and transmitted to the template for a particular student: the electrical capacity of the capacitor C, the inductance of the coil L and three resistance values for which resonant curves are taken.The output voltage of the generator E is assumed to be constant and equal to one volt.
In order for the simulation parameters generally correspond to the parameters of the real installation, it is assumed that the range of resistances used is 30-400 Ohms, the capacitance of the capacitor is 20-80 nF, the inductance of the coil is 2-50 mH.Then the resonant frequency of the circuit is within the range of 2920-25200 Hz.
The frequency of the harmonic signal of the generator can be changed in the range of 10-100000 Hz in increments of 10 Hz.The resistance of the slider rheostat in the oscillating circuit changes discretely in increments of 1 Ohm in the range of 10-500 Ohms.
Having set the specified resistance value, the student, by changing the frequency of the generator, measures the amplitude-frequency response   U  .The recorded readings of the voltmeter U are calculated according to the known formulas Having constructed a resonance curve based on the measurement results, the student determines the resonance frequency and Q-factor.

Conclusion
The approbation of the described works took place in the process of studying physics by students of the technical university.The forced transition to distance learning in the pandemic context led to the search for new forms of teacher-student interaction.The students performed laboratory work using any device available to them.It could be both a tablet and a smartphone.The individualization of the parameters of the virtual installation had a beneficial effect on the independence of work.Rare attempts to use other people's results had become immediately obvious.
The experience gained in the process of work will be useful when expanding the list of laboratory work simulators.

Fig. 6 As
Fig. 6 Fig.7 constants a and N are individual and transmitted to the template for a specific student.The number of turns of the solenoid is limited by the interval 1900 4000 N  .The known constants a and N and the exposed cathode-anode voltage U uniquely determine the values of I 0 and I C in the constructed model.To calculate the value of the anode current, the function was selected the constructed function, its graph is shown in Figure8.