College Physics

Evaluating summation of series with the resdue calculus

YANG Shi-jie

College Physics. 2024, 43(8): 4. doi:10.16854/j.cnki.1000-0712.230445

Abstract ( 300 )

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By employing the Bose and Fermi distribution functions, we introduce a method to calculate the summation of an infinite series via the residue calculus. With this method we obtain several infinite series sums and further derive the Mittag-Leffler expansions of some important functions.

Educational expansion in magnetic charge and its field

FU Chun-e1, WEI Shao-wen2

College Physics. 2024, 43(8): 7. doi:10.16854/j.cnki.1000-0712.230355

Abstract ( 316 )

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In physics, due to the symmetry between electricity and magnetism, physicists believe that magnetic charge exist in nature, similar to electric charges. Although experimental evidence for the existence of magnetic charges has not been found, discussion and exploration of this concept have never ceased. The initial focus of this article is to study the covariant form of the Maxwell's equations in the presence of magnetic charges. To do this, we classify the magnetic field into two types, i.e., Bh generated by magnetic charges and Bt produced by changing electric fields and conduction currents. Then we find that by introducing certain constraints for Bh, we can decompose the Maxwell's equations into the Maxwell's equations without magnetic charges and three additional constraint equations satisfied by Bh. The Maxwell's equations without magnetic charges naturally satisfy the principle of covariance in specail relativity theory, and we will not talk about this. We will study the properties of magnetic charges and their magnetic fields as a new form of matter by the three equations concerning Bh.

Exploring the schematic diagrams related to Nernst’s equation

SU Shan-he, CHEN Jing-yi, CHEN Jin-can

College Physics. 2024, 43(8): 10. doi:10.16854/j.cnki.1000-0712.230378

Abstract ( 169 )

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It is pointed out that the various schematic diagrams related to Nernst’s equation in textbooks are not equivalent, some of which are acceptable, some are imperfect, and some are incorrect. Moreover, the complete schematic diagrams related to Nernst’s equation are given to remedy the deficiencies in many textbooks. The results obtained are helpful to deepen the understanding of Nernst’s equation and low-temperature chemical reactions.

Proving the uniqueness theorem of electromagnetostatic field by applying action

HUANG Zhen-rui, Shi Huan-yu MIAO Rong-xin

College Physics. 2024, 43(8): 13. doi:10.16854/j.cnki.1000-0712.230423

Abstract ( 205 )

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The uniqueness theorem of the electrostatic field plays an essential role in electrodynamics. It states that the electric field can be determined uniquely, given the charge distribution and dielectric distribution of the area of our concern and given the potential or its normal derivative on the boundary. The proof of uniqueness theorem is tricky. However, most textbooks do not discuss the proof method's physical significance and the generalization to other fields. This paper finds that the action closely relates to the proof of uniqueness theorem. Once one constructs the action obeying the corresponding equations of motion and boundary conditions, one can prove the uniqueness theorem for any field. Furthermore, we discuss more general equations of motion and boundary conditions and study the case violating the uniqueness theorem.

An experimental study of transparent solution concentration based on mobile phone camera

FENG Guo-qiang1, YU Zhe-xian1, HU Ying1, XIAO Ying1, WANG Xin-ping1, DU Xing1, LI Wei2

College Physics. 2024, 43(8): 18. doi:10.16854/j.cnki.1000-0712.230366

Abstract ( 191 )

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An experimental design for the measurement of transparent solution concentration based a mobile phone camera and the principle of optical minimum deviation angle is proposed in this paper. When a laser beam passes through a hollow triple prism with different concentration solution, the outgoing light will has different angle of refraction. The outgoing light image is observed and gathered, and then transmitted to computer. The functional relationship between the liquid concentration and the angle is obtained by using the image processing technique and linear fitting. Finally, the transparent liquid concentration is successfully achieved. This design shows several merits, such as good measuring speed, accurate results, obvious phenomenon and very interesting, which is suitable for application in common physics optical experiment.

Research on polarization detection of electro-optical characteristics of nematic liquid crystals with consideration of absorption and scattering loss

YAO Feng-feng, ZHOU Yu-long, PEI Yan-bo

College Physics. 2024, 43(8): 23. doi:10.16854/j.cnki.1000-0712.230318

Abstract ( 110 )

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For nematic liquid crystal samples with a thickness of tens of microns or doped with rod-like dye molecules, anisotropic scattering and absorption will have a significant or even dramatic impact on polarization detection. The ideal polarization analysis model without considering absorption and scattering loss will no longer be applicable. In this paper, a more universal polarization detection system for measuring reorientational angle of nematic director is designed. A polarization analysis theory considering anisotropic absorption and scattering is given. A reliable and stable test scheme and a specific data processing method are given in combination with the practical testing.

The magic number “three”

ZHENG Hua1, WANG Xin-gang1, ZHU Li-lin2

College Physics. 2024, 43(8): 28. doi:10.16854/j.cnki.1000-0712.240011

Abstract ( 145 )

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The speciality of the magic number “three” in language, mathematics, and physics is discussed in general by using many examples. We emphasize the significance of the relationship between three variables. Because it is the foundation for many formulas and models; it helps us to describe and explore our world; it plays an important role for the logical thinking and generating the complex problems as well as cognitive development.

An integration model of the university-government-school collaboration: a case study of the physics community of Beijing Normal University

SANG Hai-Bo, GUO Zhi-Kuang, YAO Jian-Xin

College Physics. 2024, 43(8): 30. doi:10.16854/j.cnki.1000-0712.240137

Abstract ( 139 )

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Multifaceted collaboration for professional development of teachers is important in contemporary teacher education. In recent years, building upon the traditional bilateral cooperation model between higher education institutions and primary and secondary schools, there has been an increased focus on the localized support needed for practical work. The tripartite cooperation among universities, local governments, primary and secondary schools has become the current direction of development. In this paper it is reviewed that the literaturerelatedto the collaboration models of teacher professional development, with a systematic comparison and analysis on existing cooperation models, and examination on the reasons, characteristics, elements, and patterns of cooperation. Furthermore, by incorporating a case study of the construction of the physics community of Beijing Normal University, the integration of various cooperative models is explored

Developing cross-integrated mathematics and science education and cultivating innovative scientific thinking

YANG Ju-e1, WANG Zhi-heng2, LONG Wen-hui2, SONG Lun-ji1

College Physics. 2024, 43(8): 35. doi:10.16854/j.cnki.1000-0712.230365

Abstract ( 159 )

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With implementation of the strategy of invigorating China through science and education, the urgent need to cultivate high-level scientific research and application talents has put forward higher requirements for the reform and development of basic mathematics and science education. In this paper, focusing on the innovative scientific thinking, the analysis and description of the motion of rigid body in theoretical mechanics of physics specialty is taken as an example, and the spatial thinking embodied in abstract concepts of vector is combined with linear space in linear algebra to show and analyze how to carry out cross-integrated mathematical and science education in basic theory courses. The teaching practice of combining theoretical mechanics with linear algebra is carried out, and the problems existing in the current basic mathematics and science education are analyzed in detail. The reform of cross-integrated mathematics and science education is explored, including teaching contents, assessment methods, online and offline classroom constructions, etc. It is thus recommended to implement deeply cross-integration teaching philosophy, advocate to guide students understanding deeply the basic mathematical and science concepts and principles, change their passive acceptance of thinking habits, and stimulate their professional interest and self-cultivation awareness of original innovation ability.

Research of the nucleation of bubbles and droplets in the quark-hadron phase transition

SHI Junxi1, 2, MAO Hong3, Shu Song1

College Physics. 2024, 43(8): 42. doi:10.16854/j.cnki.1000-0712.230317

Abstract ( 130 )

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By using finite temperature field theory and F-L model, we derive the effective potential at finite temperature as well as the field equations and related physical quantities of bubbles and droplets in the first order phase transition of the quark matter. Under different boundary conditions the bubble or droplet solutions are numerically solved. Through bubble or droplet nucleation phenomenological model, the formation mechanism of bubbles and droplets in the quark/hadron phase transition is analyzed. The properties of bubbles and droplets are numerically studied by comparison through which the physical pictures and variation features of bubbles and droplets in the phase transition have been illustrated. Our methods and results may have possible applications in the study of the system of QGP phase transition for experiments on heavy ion collisions and the neutron star structures or the evolution of the cosmological phase transition in the early universe.

A normalized representation of character space based on Dirac symbols in#br# molecular point group#br#

ZHANG Shan-shan, YAN Tian-ying

College Physics. 2024, 43(8): 49. doi:10.16854/j.cnki.1000-0712.230332

Abstract ( 111 )

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Character table consisting of irreducible representations (IRs) is the basis of the group theory, and the orthonormality in irreducible representations has been proved by the great orthogonality theorem (GOT). In teaching group theory, we introduce Dirac symbols to represent irreducible representations, in order to provide a concise and easily understanding expression of the GOT. Consequently, the completeness of the character space, expanded by the irreducible representations, is expressed accordingly. On the basis of the completeness of character space, the reducible representations of the normal mode of vibrations of two molecules (H2O and NH3) are expanded by the irreducible expansions, in order to illustrate the applications of Dirac symbols in group theory. Such teaching plan is expected to help students to better understand molecular point group, symmetry operations, irreducible representations, the GOT, completeness of character space, and the decomposition of reducible representation, toward improving the quality of teaching.

Research on the motion of an unpowered moving sphere on the sand

ZUO Xue-yang, LIU Jun-ran, BAI Zai-qiao, JING Peng-fei

College Physics. 2024, 43(8): 56. doi:10.16854/j.cnki.1000-0712.230395

Abstract ( 165 )

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Based on the resistance model，this paper analyzes the classical penetration dynamics problem of an unpowered ball motion with initial velocity on a granular medium by introducing inertial resistance，viscous resistance and static resistance derived from Archimedes- modified law. A quantitative solution of the longest sliding distance of the pellet on the particle medium is obtained by means of the kinetic equation of the pellet motion. The particle density ρ_0，particle packing densityρs，particle radiusr，sphere radius R，sphere density ρb，Youngs modulus G of the particle medium are also investigated. And the influence of initial velocity v0 on the distance of small ball. It is found that the theory of resistance model is in good agreement with the experiment.

Improved experiments for measuring the viscosity coefficient of liquids

WANG Zi-ao, MOU Yi-chu, CHEN Jia-yi, TAO Zi-yang, Ning Jia-wen, CHENG Yuan, SU Yu-rong

College Physics. 2024, 43(8): 64. doi:10.16854/j.cnki.1000-0712.240102

Abstract ( 249 )

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The falling ball method is a common technique used in university physics experiment for measuring the viscosity coefficient of liquids. However，it suffers from issues，such as difficulty in ball retrieval，limitations due to the transparency of the liquid and relatively low accuracy. This improved experiment is based on the principle of conversion method in physics experiments. It involves using a pulley system to shift the velocity measurement process from inside the cylinder to the outside. Additionally，a laser rangefinder and aperture structure are introduced to measure the viscosity coefficient of castor oil at different temperatures. The experimental procedure is concise and facile，offering intuitive demonstration with high precision，particularly suitable for opaque liquids. Thereby IT bears significant potential for widespread applicability.

Calculation of relative light intensity of centers of bright stripes in Fraunhofer single slit diffraction by half-wave zone method

WANG Zhi-yuan, FAN Ling

College Physics. 2024, 43(8): 68. doi:10.16854/j.cnki.1000-0712.230274

Abstract ( 182 )

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An approximation method for directly solving the relative light intensity of centers of bright stripes in Fraunhofer single slit diffraction is presented，and an in-depth error analysis is conducted. By combining half-wave zone method and amplitude vector method，the central light intensity of bright stripes can be calculated simply and directly. By comparing different amplitude vector graphics，the error cause is analyzed. The accurate positions of bright center are obtained through quantitative analysis. It is found that the maximum relative error of this method is less than 5 %，and when the fringe order is greater than or equal to 3，the relative error is less than 1%.

Simulating the abnormal phenomena in Fraunhofer diffraction

LU Han-lin, BAI Cui-qin

College Physics. 2024, 43(8): 72. doi:10.16854/j.cnki.1000-0712.230361

Abstract ( 160 )

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In the experiment of observing Fraunhofer single-slit and multi-slit diffraction with He-Ne laser as light source，an abnormal concave shape appears at the center of the diffraction intensity distribution curve，which is inconsistent with the theoretical pattern. Considering the weak light transmission of the coating layer of diffraction plate，a non-ideal single-slit/multi-slit diffraction model is constructed under the condition of extra light transmission in the coating layer. Based on Kirchhoff diffraction formula and Gaussian beam formula，the formulas of single-slit and multi-slit diffraction of Gaussian beam under the above model are derived，and the observed abnormal phenomenon is successfully reproduced through numerical simulation. It indicates that the main cause of this phenomena is the weak light transmission of coating layer near the slit.

Analogy study of acoustic wave and electromagnetic wave reflection and refraction through eigenfunction

WU Bo-qing, ZHU Qian-yao, YU Cong

College Physics. 2024, 43(8): 78. doi:10.16854/j.cnki.1000-0712.230281

Abstract ( 125 )

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The problem of wave propagation is very common in physics, and electromagnetic waves and acoustic waves are very common types of waves. They have similar equation forms and reflection and refraction conditions, but they differ in terms of the number of polarization states and the total refraction conditions. This paper mainly uses the eigenfunction method based on quantum mechanics to carry out theoretical calculations and numerical simulations, and obtains the refraction and reflection coefficients of electromagnetic waves and acoustic waves at the interface between two media. This method is more suitable for distinguishing the propagation direction of waves and can provide advantages in solving more complex wave equations.

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