College Physics

A brief discussion on variational principle and some applications

ZHENG Shen-zhou, YU Hai-yan

College Physics. 2023, 42(10): 1. doi:10.16854/j.cnki.1000-0712.230014

Abstract ( 642 )

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The variational principle is introduced, and its Euler-Lagrange equation for the minimum of variational problems in the setting of one dimension is described. Then, the corresponding specific expression of these Euler-Lagrange equations for taking a geodesic line, geodesic curve, Brachistochrone and isoperimetric problems are deduced as examples, respectively. The solutions of the corresponding original problems are obtained and the relevant generalizations are given.

Analysis of conservation of momentum and angular momentum in collision problems

QIU Hong-mei, QIN Ji-hong, XU Mei, LIU Li-hua

College Physics. 2023, 42(10): 2. doi:10.16854/j.cnki.1000-0712.230039

Abstract ( 1053 )

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In this paper, the most typical collision problem between an object and a slender bar in rigid body mechanics is taken as an example, and the application conditions of the law of conservation of momentum and conservation of angular momentum are discussed from the perspective of force analysis, in order to deepen the understanding of the two conservation laws, hoping to play a certain reference role for teachers' teaching or students' self-study

Electronic energy spectra and wave-functions of 2D triangular quantum structures

ZHANG Li, LU Fei-yue

College Physics. 2023, 42(10): 10. doi:10.16854/j.cnki.1000-0712.220516

Abstract ( 323 )

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Using a nonseparable variable approach, the electronic energy spectra and wave-functions of 2D triangular quantum structures, including the hemi-equilateral triangle, the isosceles triangle, and the equilateral triangle are deduced and analyzed. The exact and analytical electronic states and energy-level equations in the three types of triangular structures are obtained. Numerical calculations are performed based on the material parameter of typical AlN semiconductor. The energy-level structures and wave-function distributions of electronic states are discussed in detail. The result reveals that the symmetry of the triangular quantum structure plays an important role in the energy-level structures and wave-function distributions of the triangular quantum structures

Solving Helmholtz equations in cylindrical coordinate system and its typical application in electromagnetism

MA Zi-yin, CHEN Wen-qiong, MEI Zhong-lei

College Physics. 2023, 42(10): 15. doi:10.16854/j.cnki.1000-0712.230065

Abstract ( 1043 )

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Helmholtz equation is a kind of elliptic partial differential equation, which is used to characterize the propagation law of electromagnetic wave. When solving Helmholtz equation in cylindrical coordinate system, most textbooks use the method of separating variables to introduce, but most textbooks do not have a detailed classification and discussion of the results of separating variables, nor do they explain its practical application, which makes it difficult for beginners to understand and master physical meanings. In this paper, the Helmholtz equation is solved by the method of separating variables, the form of solution is discussed systematically, and the typical applications of various results are analyzed by means of electromagnetic simulation and numerical calculation. It has a certain reference significance for the teaching and research of electromagnetic field theory.

Using Gauss variation and Jourdain variation to derive Lagrange equations of nonholonomic constraint system

ZhANG Jiu-zhu

College Physics. 2023, 42(10): 20. doi:10.16854/j.cnki.1000-0712.220589

Abstract ( 324 )

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This paper argues that it is not necessary to use the unprovable and geometrically ambiguous Chetaev（Четаев） relations to study the motion of nonholonomic constraint systems. In fact, by applying the Gauss variation to the universal equations of dynamics, the Lagrange equation can be derived for a general first-order nonholonomic constraint system using the method of Lagrange multipliers, the first-order linear nonholonomic constraint system beings only its special case; if the latter must be derived from the constraint equation, the Jourdain variation can be used. The key here is to write the equations satisfied by the imaginary acceleration, imaginary velocity and imaginary displacement respectively correctly.

Some suggestions on the introduction of polarization concept in optics

BOFang

College Physics. 2023, 42(10): 24. doi:10.16854/j.cnki.1000-0712.230001

Abstract ( 363 )

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Polarization is an important basic concept in optics courses, however, it is not easy to understand. In this paper it is suggested that during the introduction of the concept of polarization, the coordinate system, physical quantity and observation direction of light vector diagram should be explained in detail. As an extension of knowledge, the concepts of scalar beam and vector beam can also be introduced to help students grasp the concept of polarization comprehensively and accurately.

Discussion on dispersion effect in ferromagnetic resonance experiment

CHEN Sen, ZHU Bang-kai, PEI Yi-li, LI Li, RAN Yu-jing, WU Ping

College Physics. 2023, 42(10): 26. doi:10.16854/j.cnki.1000-0712.220616

Abstract ( 368 )

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In ferromagnetic resonance experiment, under the action of a stable magnetic field, the change of the permeability of samples to be measured will cause a shift of the resonant frequency ω of the resonant cavity. that is the dispersion effect, which has a significant impact on the ferromagnetic resonance curve. Transmission resonator is applied to measure the ferromagnetic resonance curve in experiment, and obvious dispersion effect appeared. Based on the influence of the ferromagnet on the natural frequency, the perturbation theory is adopted to explain the cause of the dispersion effect and its influence on the ferromagnetic resonance curve. Thus it solves a difficult point in the teaching process of ferromagnetic resonance experiment.

Measurement of polarized light: theory source tracing and data processing

LIANG Yu-lin, XING Yan-xia

College Physics. 2023, 42(10): 31. doi:10.16854/j.cnki.1000-0712.220593

Abstract ( 441 )

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polarized light can be categorized as linearly, circularly and elliptically polarized light, but the distribution of light intensity obtained in experiment is not in linear or elliptic shape, which is the so-called “linearly polarized light not linear, elliptically polarized light not elliptic”. The mismatch of intuition and experiment keeps bothering college students on the starting line of learning optics. Starting from physical essence of polarization in this article, the basic theory of polarization is traced while the linearly polarized light and elliptically polarized light are defined by mathematical performance of polarization. Then, experimental features of all kinds of polarized light is predicted by rigorous theoretical derivation. At last, by using experimental data, the nature of the polarized light, linearly polarized or elliptically polarized, can be theorical reduced.From theory to experiment and then from experiment to theory, a bridge between theory and experiment is constructed.

Research and practice of curriculum ideological and political education of mechanics in college physics

SHI Guo-fang, YANG Chao, LI Jing-ling

College Physics. 2023, 42(10): 38. doi:10.16854/j.cnki.1000-0712.220600

Abstract ( 585 )

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Curriculum ideological and political education is a strategic measure of realizing the basic task of morality education in universities. In this article, the present situation of curriculum ideological and political education is analyzed, then taking mechanics as an example, many ideological and political elements in mechanics are explored and provided from four aspects. The technique and principle during curriculum ideological and political education are also pointed out, and the result shows that curriculum ideological and political education in college physics is beneficial to the character shaping and all-round development of students. It is widely praised by students.

The design and application of modern Arago^,s disc experiment in college physics

ZHENG Qia-hao, HUANG Rui-xuan, XIAO Yuan, LU Rong-de

College Physics. 2023, 42(10): 44. doi:10.16854 /j.cnki.1000-0712.220591

Abstract ( 476 )

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Arago^,s disc is the most extraordinary experiment in the discovery of electromagnetic induction， and is also a high-quality interdisciplinary case in university physics. This paper introduces the mathematical details of modern Arago^,s disc experiment and the simple construction of experimental equipment. In the modern mode， the use of tachometer， speed regulator and electric manometer can quickly display the electromagnetic damping and driving effect， and the convenient mode that can replace disks or wire meshes of different metal materials is selected so as to promote its use and promotion in classroom and experimental teaching.

A demonstration setup for superconductor levitation based on 3π-Mbius strip track

CHEN Gan-yu, WANG Miao, YANG Cheng-wen, BI Xiang-yu, QIN Feng, QIU Cai-yu, YUAN Hong-tao,

College Physics. 2023, 42(10): 50. doi:10.16854 /j.cnki.1000-0712.220535

Abstract ( 477 )

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Superconductor levitation refers to the phenomenon in which a superconductor levitates due to its diamagnetic nature， when put in an external magnetic field. This mechanical equilibrium is achieved when gravity balances out electromagnetic force exerted on superconductor by permanent magnets. In this paper a demonstration setup for superconductor levitation via a neodymium-magnet-based 3π-Mbius strip track is introduced. The superconductor may levitate above， move along， rotate about and suspend below the track. Parameters including magnetic field distribution and electromagnetic force， such as geometry of the track and maximum energy product of the magnets， are optimized. A demonstration duration of 10 minutes is achieved by using a YBa2Cu3O7 superconductor， and this setup is a valuable asset to science exhibitions and demonstration of superconducting physics.

Constructing irreducible representations of a finite group using induced representations of its invariant subgroups

HU Jia-hang, JI Jun-yi, XIANG Hong-jun, LI Xin-zheng

College Physics. 2023, 42(10): 59. doi:10.16854 /j.cnki.1000-0712.220465

Abstract ( 318 )

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This paper introduces a method of constructing all inequivalent irreducible representations of a finite group using induced representations of its invariant subgroups，and applies it to the solution of the character table of the first kind of crystal point groups. This method is systematic and simple，and can be used as a supplement to the method of solving irreducible representation of the point groups in current textbooks.

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