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The polytropic (adiabatic) index for pure hydrogen plasma is analytically calculated as function of reciprocal temperature and degree of ionization. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the mono-atomic value 5/3 are measurable. The analytical result for pure hydrogen plasma is a test example how this approach can be extended for arbitrary gas cocktail., Comment: 5 pages, 4 figures, 32 refs

The temperature dependence of rates of electron impact ionization and two electrons recombination are calculated using Wannier cross section of electron impact ionization of neutral hydrogen atom. Entropy production and power dissipation are derived for the case when the ionization degree deviates from its equilibrium value. This is the special case of the obtained general formula for entropy production accompanying chemical reactions. Damping rate of the sound waves is calculated and the conditions when ionization processes dominate are considered. A quasi-classical approximation for the heating mechanism of solar chromosphere is proposed. Several analogous phenomena for damping rates in liquids and crystals are shortly discussed, for example, deaf sound of a glass of beer or English salt solution. An explicit expression for the second or bulk (or volume) viscosity of hydrogen plasma is calculated from firsts principles. For the first time some second viscosity is calculated from first principles., Comment: Mandelstam-Leontovich theory applied to hydrogen plasma, 13 pages, 5 figs, 32 references

This is the problem of the 7-th international Experimental Physics Olympiad "The Day of the Inductance". A large inductance made by a general impedance converter is measured by the Maxwell-Wien bridge. The youngest students (S category) have the problem to measure the parameters of the elements in the experimental set-up. The students at middle age (category M) should balance a Wheatstone bridge with resistors only. The inductance measurement is supposed to be accomplished by the students from the upper age (L category) only. From the university students (XL category) we expect error estimation and professionally made measurement protocol. As a homework problem (Sommerfeld price) the general formula for the impedance of the general impedance converter, where the general equation for operational amplifiers is included, has to be derived. Problems for further work are also given in the text. The described set-up can be considered as a prototype for companies producing laboratory equipment., Comment: Final editorial corrections in all files

For the first time the cumulative distribution function of the crossover frequency of a contemporary operational amplifier ADA4898-2 is experimentally studied. Using a USB Lock-In amplifier, which allows automatic frequency sweep of the current response of a non-inverting amplifier with significant static amplification, we measure the crossover frequency of 200 samples of ADA4898-2 operational amplifiers. This new method gives a significant advantage in accuracy and speed of study of every operational amplifier. The theory we use is based on the universal relation between time dependent output and input voltages. This common relation for all operational amplifiers is applicable for frequencies much smaller than the crossover frequency and the frequencies of non-dominant poles. In other words, this approximation is adequate, when an operational amplifier is included in a circuit with significant amplification., Comment: 11 pages (additional discussion provoked by reviewers and editors), 5 figures, 29 refs, obtained data of this research has been added in a 7z archive file

Several consecutive experiments with specifically built set-up are described. Performing of the consecutive experimental tasks enables possibility to determine Boltzmann's constant $k_\mathrm{_B}$. The fluctuations of the voltage $U(t)$ of series of capacitors connected in parallel with a constant resistance are measured. The voltage is amplified 1~million times $Y=10^6$. The amplified voltage $YU(t)$ is applied to a device, which give the voltage mean quared in time $U_2=\left<(Y U(t))^2\right>/U_0$. This voltage $U_2$ is measured with a multimeter. A series of measurements gives the possibility to determine the Boltzmann's constant from the equipartition theorem $C\left=k_\mathrm{_B}T$. In order to determine the set-up constant $U_0$ a series of problems connected with Ohm's law are given that are addressed to the senior students. For the junior high school students, the basic problem is to analyse the analog mean squaring. The students works are graded in four age groups S, M, L, XL. The last age group contains problems that are for university students (XL category) and include theoretical research of the set-up as an engineering device. This problem is given at the Fifth Experimental Physics Olympiad "Day of the Electron", on December 2017 in Sofia, organized by the Sofia Branch of the Union of Physicists in Bulgaria with the cooperation of the Physics Faculty of Sofia University and the Society of Physicists of the Republic of Macedonia, Strumica., Comment: Further minor corrections are made. Text in English 17 pages, text in Bulgarian 18 pages, 11 figures and 3 tables per language

Several consecutive experiments are described with a printed circuit board PCB set-up, especially designed for these experiments. Doing the consecutive experimental tasks opens up possibility to determine the value of electron charge $q_e.$ The fluctuations of the voltage $U(t)$ should be measured for different illuminations of a photodiode. The voltage is amplified 1 million times $Y=10^6$. The amplified voltage $YU(t)$ is applied to the device, which gives the result of the value of the time averaged square of the voltage $U_\mathrm{S}=\left<(Y U(t))^2\right>/U_0$. This voltage $U_\mathrm{S}$ is measured with a multimeter. The series of measurements gives the possibility to determine the $q_e$ using the well known Schottky formula for the spectral density of the current noise $(I^2)_f=2q_e\left.$ For the junior high school students, the basic problem is to analyze the analog squaring. Students' work is separated and graded in four categories S, M, L, XL divided by age of students. For the last XL categories, the tasks contain problems oriented to physics university education program and include theoretical research of the PCB set-up as an engineering device. This is the problem of EPO6, December 2018 ``Day of the Charge'' considered. EPO6 is organized by Sofia branch of Union of physicists in Bulgaria in cooperation with Faculty of physics of Sofia University and Society of Physicists of Republic of Macedonia., Comment: 54 pages, 6 languages (English, Bulgarian, Macedonian, Serbian, Russian, German), 2 solutions (English and German), 49 figures total, 11 tables, 4 appendices

The classical macroscopic Maxwell equations are approximated. They are a corollary of the multipole expansion of the local electrostatic potential up to dipolar terms. But quadrupolarization of the medium should not be neglected if the molecules which build up the medium possess large quadrupole moment or do not have any dipole moment. If we include the quadrupolar terms in Maxwell equations we obtain the quadrupolar analogue of Poisson's equation: $\nabla^2 \phi - L^2_Q\nabla^4 \phi = - \rho / \varepsilon$. This equation is of the fourth order and it requires not only the two classical boundary conditions but also two additional ones: continuous electric field and the relation of the jump of the normal quadrupolarizability at the surface to the intrinsic normal surface dipole moment. The account of the quadrupole moment of the molecules leads to significant differences compared to the classical electrostatic theory., Comment: Presented at the 3rd National Congress on Physical Sciences, 29 Sept. - 2 Oct. 2016, Sofia, Bulgaria