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Home experiment: fractal geometry of crumpled paper ball LUO Jie, QIAN Jun College Physics    2021, 40 (10): 73-.   DOI: 10.16854 / j.cnki.1000-0712.200522 Abstract （1555）      PDF（pc） （267KB）（795）       Knowledge map    Save During the pandemic period，experiments in home are set up in basic physics experiment course. Because of the simple preparation and easy measurement，the hand-crumpled paper ball experiment is chosen by many students. In this paper the fractal in the experiment of crumpled paper balls is discussed. The definition of fractal dimension is introduced to describe the internal irregularity of the crumpled paper balls. The fractal dimen- sion of normal A4 printing paper is measured experimentally and the influence of different paper hardness and paper layers on the fractal dimension of paper ball is studied. Related Articles | Metrics

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Electrodynamic explanation of faraday magneto-optical rotation effect XIAO Tian-ning, WANG Shuan-hu College Physics    2021, 40 (9): 72-.   DOI: 10.16854 / j.cnki.1000- 0712.210068 Abstract （1077）      PDF（pc） （463KB）（267）       Knowledge map    Save Faraday magneto-optical rotation effect is a phenomenon that applying an external magnetic field to an isotropic medium will induce the optical rotation property. In this paper， light is regarded as an electromagnetic wave. By using the method of electrodynamics， starting from the equation of motion of electrons in an isotropic me- dium under an external magnetic field， the change of the system caused by the magnetic field will be analyzed. And then the relative dielectric tensor is obtained， which is solved by combining with Maxwell equations. By using the simple knowledge of electrodynamics， we can strictly deduce that the eigenstates of magneto-optical system must be right-handed and left-handed polarization. Furthermore， we can make readers better understand the source of fara- day effect in the perspective of eigenvalue problem. Related Articles | Metrics

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Dirac δ-function and its related applications ZHENG Shen-zhou, KANG Xiu-ying College Physics    2021, 40 (7): 25-.   DOI: 10.16854 /j.cnki.1000-0712.200456 Abstract （1061）      PDF（pc） （299KB）（354）       Knowledge map    Save It is indicated that Dirac δ-function is a continuation of the discrete Kronecker δ-function，which plays an important role in both mathematics and physics. In this paper，the precise definition of Dirac δ-function is introduced based on the concept of generalized functions，and it is proved that the Dirac δ-function is not a usual function in the Lebesgue sense of local integrable one. To this end，the Dirac δ-function is here approximated in the sense of weak limit by making use of the sequences of the unit rectangle impulse functions，Gauss functions，Bell- shaped functions and Sinc-functions，respectively. In addition，it is checked that the Dirac δ-function is obtained as a generalized derivative of the Heaviside function，and its higher derivative is also shown. Moreover，the convo- lutions，scales，compound transformations，orthogonality and Comb Dirac functions are recalled，respectively. Fi- nally，the relationship between Dirac δ-function and generalized Fourier transform is introduced，and we present an application to solve the Dirichlet boundary value problem of the Poisson equation. Related Articles | Metrics

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A deduction method of mass-velocity relationship in special theory of relativity FENG Shi-meng College Physics    2021, 40 (6): 32-.   DOI: 10.16854 / j.cnki.1000-0712.200506 Abstract （853）      PDF（pc） （616KB）（271）       Knowledge map    Save The mass-velocity relationship is an important conclusion of the theory of relativity. Most textbooks use two objects to collide completely in-elastically for observing the speed change from different frames of refer- ence，and obtain the mass-speed relationship. This paper uses the Lorentz transformation of space-time in the spe- cial theory of relativity to prove the invariance of the force in the direction of motion in the two inertial reference frames. Then，Newton's second law is directly to derive the relationship between mass and speed. This derivation method is relatively simple. which is very conducive to the understanding of junior college students. Related Articles | Metrics

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vibration law of Wilberforce pendulum JIANG Fu-jin¹, HAN Can² College Physics    2021, 40 (11): 15-.   DOI: 10.16854 / j.cnki.1000-0712.210083 Abstract （780）      PDF（pc） （685KB）（582）       Knowledge map    Save In this paper，a possible vibration model is conjectured according to the vibration characteristics of Wilberforce pendulum. Based on this model，the dynamic differential equations of Wilberforce pendulum are written out. Then the normal frequency and the analytical solution of the vibration are obtained. Finally，the numerical sim- ulation of the analytical solution is carried out and compared with the experimental data，which proves the rationali- ty of the conjecture Related Articles | Metrics

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Spherically averaging function and deduction of its differential equation CAI Jun, LI Min, WANG Qun College Physics    2021, 40 (8): 16-.   DOI: 10.16854 / j.cnki.1000-0712.210016 Abstract （764）      PDF（pc） （187KB）（291）       Knowledge map    Save The initial- value problem of the wave equation in the three-dimensional case is a very important content in the course of methods of mathematical physics. In this paper，we discuss the definition of the spherically averaging function and how to build up the partial differential equation satisfied when we use the method of spherical means to solve this problem. A more concise procedure to deduce the equation of spherically averaging function is provided based on the analysis of the deduction appeared in the textbooks. Our discussion will clarify the basic meaning of the spherically averaged function and is benefit to the teaching and studying of the method of spherical means and other solutions to the equations of mathematical physics in three-dimensional spherical coordinates. Related Articles | Metrics

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Influence of spectrometer adjustment on the measurement of apex angle and minimum 　　deviation angle of a triangular prism LI Xin-jing, SONG Xin-bing College Physics    2021, 40 (8): 72-.   DOI: 10.16854 / j.cnki.1000-0712.200448 Abstract （734）      PDF（pc） （459KB）（264）       Knowledge map    Save In the experiment of measuring the refractive index of a prism with a spectrophotometer，a key step is to adjust the object stage so that its main axis is perpendicular to the optical axes of the telescope and the collima- tor，which is called the standard case. It is analyzed that the influence on the measurement of apex angle and mini- mum deviation angle theoretically and experimentally when there is a deviation of the object stage. The experiments are performed for two cases. One case is that，in the telescope，it can be found that a green cross image reflectes from at least one surface of the double face plane mirror. In this case，the deviation is marked by recording the posi- tion of the green cross image. The other case is that the deviation of the object stage is measured with an extra sys- tem. In this case，the deviation degree of the object stage can be recorded directly. In experiment，the variation of the apex angle and minimum deviation angle of the prism with the deviation of the object stage is measured in the two cases. And the object stage’s deviation range，at which the experimental results has smaller deviations than standard measurement errors，is determined. Related Articles | Metrics

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Thoughts on the ideological and political construction of electrodynamics course WANG Zhen-lin College Physics    2021, 40 (6): 53-.   DOI: 10.16854 /j.cnki.1000-0712.210010 Abstract （710）      PDF（pc） （1283KB）（490）       Knowledge map    Save  In this paper，it is illustrated the facts that scientific development benefits from an innovation culture of society and the original innovation makes great impact on science and technology，and promotes social development from the perspective of the history of electrodynamics. Furthermore，it is demonstrated that the rich ideological and political connotations of electrodynamics，including the spirit of science in exploring nature and the value orientation of serving the society. Centering on !imparting knowledge，preaching truth，dispelling doubts，and fostering virtue'，the thoughts and observations on the ideological and political connotations of this course were shared in this paper. Related Articles | Metrics

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Superconducting quantum bits SU Fei-fan¹, YANG Zhao-hua¹, ², FAN Heng¹, ², ZHAO Shi-ping¹, ² College Physics    2021, 40 (7): 1-.   DOI: 10.16854 /j.cnki.1000-0712.210045 Abstract （664）      PDF（pc） （482KB）（424）       Knowledge map    Save With Google's successful demonstration of " quantum supremacy" in 2019，the research of supercon- ducting quantum computing is attracting more and more attention around the globe. Superconducting quantum bits ( qubits) are macroscopic devices with fundamental quantum properties such as energy-level quantization，quantum- state superposition and quantum-state entanglement. They provide an excellent platform for the studies in many fields such as quantum physics，atomic physics，quantum optics，quantum chemistry，quantum simulation，quantum computing，and so on. In this article，we discuss the basic principles and structures of the superconducting phase-， charge-，transmon-，and flux-type qubits，as well as their device design and fabrication process. We also present a brief introduction to the rich research areas based upon the superconducting qubit architecture. Related Articles | Metrics

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Design experiment of university physics: research on demonstration device of Lissajous graphic WU Han¹, YU Yao¹, YOU Yin-tao¹, TANG Yong-jun¹, ZHANG Jin-long² College Physics    2021, 40 (10): 36-.   DOI: 10.16854 / j.cnki.1000-0712.210147 Abstract （658）      PDF（pc） （276KB）（262）       Knowledge map    Save In this paper，a comprehensive design experiment of university physics，the self-making Lissajous graphic demonstration device is introduced. The reason why Lissajous figures is formed through theoretically analy- zing the thin film ' s forced vibration. The experimental results show that the shape and size of Lissajous figures change periodically when the frequency of the sound source increases. Finally，the effective surface tension value is estimated to be about 46.00 N / m through the measured resonance frequency when the surface area of latex ballon is twice the normal area，indicating that the device has certain practical applicability. Related Articles | Metrics

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Dynamic analysis of dancing coin HU Li College Physics    2021, 40 (7): 75-.   DOI: 10.16854 / j.cnki.1000-0712.200366 Abstract （650）      PDF（pc） （244KB）（729）       Knowledge map    Save From the perspective of dynamics，this paper conducts a theoretical analysis on the third problem of the 2018 International Young Physicists’Tournament ( IYPT2018) ，“Dancing Coin”，and obtains the change in the height of the coin over time during a single beating. At the same time，the concept of “place error”is pro- posed，and the influence of coin place error on the coin’s tilting height is further discussed. It is found that the greater the place error，the faster the coin will rotate and the greater the maximum height of the coin will be reached. In the experiment，the process of coin dancing under different place errors was recorded with a high-speed camera，and software tracker was used to track. The comparison between the experimental results and the theoretical model verifies the correctness of the theoretical model. Related Articles | Metrics

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Green functions and their applications to ordinary differential equations QIAN Guang-yao, YAN Ruo-kun, WANG Ze-xi, ZHENG Shen-zhou College Physics    2021, 40 (9): 81-.   DOI: 10.16854 / j.cnki.1000- 0712.210142 Abstract （614）      PDF（pc） （460KB）（243）       Knowledge map    Save In this paper， we are devoted to a review of the Green functions and the Green 　　function method for solving the initial and boundary value problems of various ordinary 　　differential equations. For the initial value prob- lem of linear ordinary differential equation 　　of first order， the formula of Green function and the solution represented 　　by Green function are given. For the boundary value problem and initial value problem of linear 　　ordinary differential equation of second order， the calculation of Green function and the 　　solution represented by Green function are shown， respectively. The calculation of Green 　　function and the solution representation by Green function for Sturm- 　　Liouville problem satisfying general initial value conditions are established. For the 　　un-mixed and mixed boundary value problems of linear ordinary differential equations of second 　　order， we also consider how to find Green function and the solution represented by Green 　　function， respectively. Finally， For the boundary value problem of higher or- der linear ordinary 　　differential equations， the Green function and the solution expressed by Green function 　　are ob- 　　tained. Related Articles | Metrics

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A new data processing method for Newton ring interference experiment HUA Xiao-bin, HUA Shi-qun College Physics    2021, 40 (7): 35-.   DOI: 10.16854 / j.cnki.1000-0712.200471 Abstract （607）      PDF（pc） （213KB）（195）       Knowledge map    Save Based on Newton’s ring interference experiment，the air layer thickness difference in the vertical direction between two adjacent interference rings is half wavelength. By taking the diameters of interference rings measured by moving reading microscope as horizontal coordinates，and taking the air layer thickness differences de- termined by the order difference of interference rings as longitudinal coordinates，the large circle equation of the planoconvex lens sphere in Newton’s ring device can be fitted and used to obtain the curvature radius of the plano- convex lens sphere. The experimental results show that the new experimental data processing method needs less measuring points，the process is simple and the results are reliable. Related Articles | Metrics

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Influence of the waveform distortion of magnetic field intensity on the shape of AC hysteresis loops LV Qing-rong, FENG Shuang-jiu College Physics    2021, 40 (6): 45-.   DOI: 10.16854 / j.cnki.1000-0712.200424 Abstract （600）      PDF（pc） （1464KB）（99）       Knowledge map    Save AC hysteresis loops of soft ferrite ring sample are measured under different conditions. It is found that the shape of the hysteresis loops changes with the amplitude and frequency of AC magnetic field strength. The changes of the shape of the AC hysteresis loops are caused by the waveform distortion of magnetic field intensity H. In a weak AC magnetic field，when magnetic induction intensity B is changed sinusoidally，the magnetic field intensity H is also changed sinusoidally. At this time，the shape of the hysteresis loop is elliptical. When the mag-netic field intensity increases，H-t curves show different degrees of distortion. The stronger the magnetic field is， the more severe the distortion of H - t curves is. At this time，the shape of hysteresis loops becomes bended and sharp，shows a fat“S”shape. These changes in the shape of hysteresis loops are explained through theoretical anal-ysis and experimental fitting. Related Articles | Metrics

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Systematic error analysis of period of simple pendulum SHAO Yun College Physics    2022, 41 (1): 32-.   DOI: 10.16854 / j.cnki.1000-0712.210247 Abstract （591）      PDF（pc） （353KB）（146）       Knowledge map    Save This paper analyzes and calculates the influence of the pendulum angle，the rotation of the ball，the mass of the suspension line，the air buoyancy and the air resistance on the period of the pendulum one by one. Tak- ing a 1 m length and 5° swing angle small amplitude pendulum as an example，the relative errors of the five factors are +0.45‰，+0.02‰，-0.45‰，+0.07‰，-0.14‰，respectively，and the total is only -0.05‰，which means that the five error factors almost cancel each other，and the systematic error of the small pendulum experiment is very small in theory. This paper gives a more detailed reasoning，calculation and analysis process，especially the reasoning process of air resistance moment，as well as charts and tables，for providing a more complete and accu- rate understanding. Finally，some necessary explanations are given in view of some possible deficiencies in people's understanding of air resistance. Related Articles | Metrics

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Application of MATLAB to the study of quantum mechanics ZHOU Qun-yi¹, MO Yun-fei², ZHOU Li-li⁴, HOU Zhao-yang³ College Physics    2021, 40 (6): 19-.   DOI: 10.16854 / j.cnki.1000-0712.200527 Abstract （556）      PDF（pc） （1079KB）（226）       Knowledge map    Save This paper points out some errors in the article of “Commonly using mathematical tools in the course of quantum mechanics”and lists the correct formula. There are many formulas in quantum mechanics，while the optimal tool for solving calculation problems should be MATLAB. In this paper，with help of MATLAB，we have illustrated the algorithm of limit，the algorithm of integration，the solution of ordinary differential equations，the representation and algorithm of Dirac function，the usage of gamma function and beta function，and the algorithm of special functions. One-dimensional linear harmonic oscillator has been taken as an example，which can reflect the application of MATLAB in quantum mechanics. MATLAB can also calculate and show the graphics about the proba- bility density of the emergence of electrons in hydrogen atoms. Related Articles | Metrics

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Exploration and integration of ideological and political elements in college physics teaching ZHU Xian-zhong, CHEN Fei-ming, FENG Cun-fang College Physics    2021, 40 (6): 66-.   DOI: 10.16854 /j.cnki.1000-0712.200423 Abstract （554）      PDF（pc） （805KB）（338）       Knowledge map    Save How to excavate ideological and political education ( IPE) resources which richly containe in college physics and to exert them on students in an imperceptible way，is an urgent problem for physics teachers to solve. According to the content of college physics course，the content system of IPE with its structural relationship is combed in this paper，which embodes the political and epochal features. Two searching methods of IPE materials are provided，and the educational function of the same important IPE materials in the knowledge system of physics is analyzed in order to provide basic ideas for constructing IPE material resources. Some methods of integrating the elements of IPE in the process of teaching implementation are discussed so as to provide support for the implementation of recessive teaching strategy. Related Articles | Metrics

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Solving the continuous collisions by the phase space trajectory LI Kai-wei College Physics    2021, 40 (6): 11-.   DOI: 10.16854 / j.cnki.1000-0712.200420 Abstract （552）      PDF（pc） （764KB）（224）       Knowledge map    Save When two objects occur multiple successive collisions，the solution becomes complicated. This paper proposes the method of phase space trajectory to solve the problem and make the motion process visual. The caculation is also to be easy. Related Articles | Metrics

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Study on the Ampere circuital theorem in stationary magnetic fields HU Xi-kui, LI Li, FENG Chun-bao, MOU Qiong College Physics    2021, 40 (8): 20-.   DOI: 10.16854 / j.cnki.1000-0712.200523 Abstract （547）      PDF（pc） （267KB）（274）       Knowledge map    Save The Ampere circuital theorem is an important law in stationary magnetic fields and is often used to analyze the magnetic flux intensity of a current system with a certain symmetry. The useful conditions of the Ampere circuital theorem and its mathematical principles are studied. The misunderstanding that the Ampere circuital theo- rem is incorrect in a finite-length current-carrying straight wire system is clarified through a simple model. The uni- versality of the Ampere circuital theorem is exemplified. It helps students to master Ampere circuital theorem and understand the properties of magnetic fields. Related Articles | Metrics

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A new definition of Lie derivative HE Xiao-kai¹, CAO Zhou-jian² College Physics    2021, 40 (7): 8-.   DOI: 10.16854 / j.cnki.1000-0712.210091 Abstract （540）      PDF（pc） （160KB）（213）       Knowledge map    Save Lie derivative is an important concept of differential geometry. It is widely used in mathematics and physics. The Lie derivative is defined through the push-forward and pull-back maps. In this paper，a new definition of Lie derivative is presented. Instead of the abstract maps，we firstly introduce the concept of an adapted coordinate system of a smooth vector field on a manifold. Then a new definition of Lie derivative is given based on an adapted coordinate. It can be shown easily that the new definition is independent of the specific choice of an adapted coordi-nate system. After that，we deduce the explicit expression of the Lie derivative in general coordinate system，which admits the same form as the Lie derivative definition in usual textbooks. Compared to the existing definition of Lie derivative in usual textbooks，our new definition is much easier for beginners to understand. Related Articles | Metrics

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Notes on the principles of quantum mechanics YANG Shi-jie College Physics    2021, 40 (11): 1-.   DOI: 10.16854 / j.cnki.1000-0712.210122 Abstract （537）      PDF（pc） （244KB）（443）       Knowledge map    Save The principles of quantum mechanics as well as basic concepts and classical correspondence are re- examined from advanced point of views. We also discusse the relation between Planck constant and representation transformation. Related Articles | Metrics

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Design and practice of ideological and political education in the teaching of electromagnetic field and electromagnetic wave SONG Ling-ling, HUANG Wen College Physics    2021, 40 (11): 36-.   DOI: 10.16854 / j.cnki.1000-0712.210201 Abstract （532）      PDF（pc） （448KB）（437）       Knowledge map    Save Based on Gauss theorem in electromagnetic field and electromagnetic wave，in this paper the design of teaching with teachers as the main body is carried out，in which there are five teaching links: introduction，es- tablishment，breaking，extension and conclusion，so as to realize the teaching conception of knowledge inheritance and ability migration. Integrating the ideological and political elements into the curriculum from three dimensions not only solve the teaching difficulties，such as determining the size of the spatial angle，the key meaning of positive and negative，and the calculation of the spatial angle of closed surface，but also guide students to see problems from multiple perspectives，and help students to establish a correct outlook on life，values，and the world，so as to real- ize the goal of condensing the knowledge in the value dissemination and realizing value guidance in the knowledge dissemination. Related Articles | Metrics

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Understanding time and space connotation of Lorentz transformation by geometry ZHANG Liang College Physics    2021, 40 (6): 36-.   DOI: 10.16854 / j.cnki.1000-0712.200490 Abstract （527）      PDF（pc） （885KB）（213）       Knowledge map    Save Lorentz transformation is the core content of special relativity. It is of great significance to understand and master the conceptual connotation of Lorentz transformation for further understanding the space - time view of special relativity. In this paper，the nature of time-space transformation called clock slowing and scale reduction and the speed of light invariance condition are studied based on the two-dimensional rotation of the space-time dia- gram. It enables students to understand the Lorentz transformation more intuitively and lays the foundation for subse- quent courses. Related Articles | Metrics

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Three-dimensional simulation and visualization of the motion of rigid body and discussion on physical pendulum related problems LIN Jiong-hui¹, LIU Yu-ying², SONG Min² College Physics    2021, 40 (7): 68-.   DOI: 10.16854 / j.cnki.1000-0712.200404 Abstract （526）      PDF（pc） （710KB）（247）       Knowledge map    Save In this paper，the rotational motion of rigid body around a fixed axis is studied by using Newton’s second law for rotation and in angular form with VPython software. Some special examples discussed in detail are motions of rotating uniformly rod under different torques，the path，angular displacement，angular velocity and mov- ing process，and were visualized intuitively in real time. The conservation of the energy of rotating rigid rod only ex- perienced with torque of gravity can be verified by VPython software. The plane motion of rigid body ( translation plus rotation) and vibration of rigid body are also studied. Especially，the chaos state of rigid rod with large rotating angle is investigated. The simulation deepens the understanding of textbook knowledge. Related Articles | Metrics

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Thermodynamics and geometry LIU Quan-hui College Physics    2021, 40 (8): 1-.   DOI: 10.16854 / j.cnki.1000-0712.210029 Abstract （524）      PDF（pc） （244KB）（663）       Knowledge map    Save The interesting connections between thermodynamics and geometry have all but vanished from the literature.Three thermodynamic issues are treated with geometry.The first is how to geometrically interpret the Thom- sen-Berthelot principle，leading to the third law of thermodynamics.The second is why the van der Waals parame- ters a and b depend on the temperature once the equation of state is viewed as a two-dimensional surface.The third is that the thermodynamic fluctuations permit metric representations associated with the Riemann geometry，and the van der Waals equation of state is used to demonstrate the scalar curvature measures the interactions.Attempts to un- derstand the thermodynamics within geometry do not only offer an effective teaching and learning，but also may be helpful to find new research areas. Related Articles | Metrics

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Theoretical analysis and visualization research on uniformity distribution of magnetic field in a finite solenoid ZHOU Xiao-yan, LIU Shi-kun, ZHANG Shu-tian, SUN Min, LU Jian, HUANG De-cai College Physics    2021, 40 (6): 76-.   DOI: 10.16854 /j.cnki.1000-0712.200496 Abstract （511）      PDF（pc） （1533KB）（166）       Knowledge map    Save The magnetic field of solenoid with length L = 200 mm is discussed in detailby using the Biot-Savart law and the principle of vector superposition.The magnetic fieldof a single current-carrying circular coil is exactly derived. Pythonis adopted to integrate the analytical expressions and visualize the corresponding magnetic induction line. Compared to the classical physics textbooks，both the theoretical derivations and the numerical solutionsare verifiedvalidly. Then the same analysis are carried out on both the magneticfield and the visualization of magnetic induction line of a finite current-carrying solenoid. The influence of coildensity and solenoid length on the uniformity of magnetic field are discussed in detail. It is found that the magnetic field is regarded as uniformity in the range of -74 mm ≤ z ≤ 74 mm of a solenoid when the density is greater than 1000 m-1 . The results in this paper provide intuitive and clear teaching materials for theoretical and experimental teaching in College Physics. Related Articles | Metrics

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Solutions for a familiar mechanical problem SU Guo-zhen College Physics    2021, 40 (6): 5-.   DOI: 10.16854 / j.cnki.1000-0712.200346 Abstract （509）      PDF（pc） （861KB）（406）       Knowledge map    Save New solutions for a mechanical problem relating to the harmonic oscillation are presented based on a deep analysis. Related Articles | Metrics

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A brief analysis of the method for constructing the structures of twisted graphene bilayers CHEN Ming-xing College Physics    2021, 40 (8): 8-.   DOI: 10.16854 / j.cnki.1000-0712.210060 Abstract （495）      PDF（pc） （381KB）（290）       Knowledge map    Save Twisted graphene bilayer has been a hot topic in condensed matter physics.Here，a method for con- structing the geometric structure of graphene supercells is illustrated，which makes use of the translational symmetry of crystal and the transformation matrix between the supercell and the primitive cell. Then，the method is applied to construct the structure of twisted graphene bilayers. This system can be used as an example in the lecture of solid state physics，which is helpful for students to achieve a better understanding of the mathmatic method of describing the geometric structure of crystals. Related Articles | Metrics

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Further study on vector properties of angular displacement WANG Jing-zhou College Physics    2021, 40 (7): 12-.   DOI: 10.16854 / j.cnki.1000-0712.200488 Abstract （494）      PDF（pc） （244KB）（223）       Knowledge map    Save Discussion on vector properties of angular physical quantity，through graphic comparison，or through formula calculation，many papers draw the conclusion that infinitesimal rotation is vector and finite rotation is not vector.Neither point out the physical fundamental reason. According to the invariance of physical quantity and the covariance of transformation，it is proved that the rotation vector is not true vector，that of the essential reason is the levorotation and dextrorotation of the coordinate system. Related Articles | Metrics

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Applications of time-space diagram to special relativity teaching XU Guang-zhi, LI Yi-jie College Physics    2021, 40 (6): 26-.   DOI: 10.16854 / j.cnki.1000-0712.200417 Abstract （493）      PDF（pc） （876KB）（151）       Knowledge map    Save This paper introduces the approaches of quantitative calculation using the Minkowski time-space di- agram in special relativity. Formulas are derived for velocity addition，light Doppler effect，aberration of light and so on. Related Articles | Metrics

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Diffraction and splitting function of phase grating ZOU Yi-yun, LIN Jia-li, LU Yue-yuan, YAN Xiao-na College Physics    2021, 40 (11): 64-.   DOI: 10.16854 / j.cnki.1000-0712.210104 Abstract （490）      PDF（pc） （407KB）（125）       Knowledge map    Save Using the coherent superposition，diffractions are deduced when a plane wave incidents on a phase grating. Results show that the ±1 order diffraction of the phase grating can get the maximum intensity and realize the splitting function，overcoming the problems in amplitude grating where the 0 order diffraction has the maximum in- tensity but with no splitting function. The diffraction efficiency of ±1 order diffraction with respect to the duty ratio and phase introduced by the phase material are discussed. The method we provided here has implicit physical mean- ings and is easy to adapt to other diffraction structure. Related Articles | Metrics

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Theoretical models and an imaging experiment of the laser speckle drift phenomenon GUO You-xi, HE Yun-bo, LIU Rong-zhen, GONG Dian-jin-feng, XIA Cheng-jie College Physics    2021, 40 (7): 78-.   DOI: 10.16854 / j.cnki.1000-0712.200524 Abstract （487）      PDF（pc） （511KB）（283）       Knowledge map    Save A numerical method of calculating objective and subjective laser speckle patterns are developed based on the principles of Fourier optics. Expressions for the drift velocities of laser speckle and light spot in a sub- jective pattern are derived based on geometrical optical principles. Devices of imaging experiments are set up to ob- serve the objective and subjective laser speckle patterns and their respective drift phenomena. Methods to quantify the drift velocities of speckles and spots are established based on image processing techniques，which combine cor- relation function，the Fast Fourier Transform algorithm and convolution theorem. Both experimental and numerical results match perfectly with our theoretical expressions，which validates the numerical method and geometrical opti- cal model. This work provides a systematic method to research and an intuitive way to understand the laser speckle drift phenomenon. Related Articles | Metrics

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Practical research on the application of mind map in university science courses teaching—taking the course “Introduction to laser technology”as an example LI Hong-yu¹, XU Lin-xin², Hou Dan¹ College Physics    2021, 40 (7): 55-.   DOI: 10.16854 / j.cnki.1000-0712.200458 Abstract （474）      PDF（pc） （467KB）（122）       Knowledge map    Save Through tutoring students to preview，arranging homework and collecting feedback in teaching the course of introduction to laser technology，the teacher let students freely choose whether to use mind map or not to complete homework and gradually guided students to try to use it to summarize knowledge points. These measures stimulated students’interest in applying mind map as a learning tool，and also made students’enthusiasm improved in learning the course of introduction to laser technology. It is also found that the mode of mind map plus notes not only took advantages of mind map to help clarify knowledge context，but also remedied the shortcomings that mind map could not show the specific content of knowledge points with notes. Therefore，this mode is more suitable for the study of physics subjects when compared with the simple mind map mode. Related Articles | Metrics

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Development and application of physical animation based on HTML5 technology SONG Hong-xiao¹, ZHANG Qi-wei², LIU Jian-qiang¹ College Physics    2021, 40 (7): 51-.   DOI: 10.16854 / j.cnki.1000-0712.210005 Abstract （468）      PDF（pc） （309KB）（104）       Knowledge map    Save With mobile devices such as mobile phones replaced computers as the mainstream way of surfing the internet，the Flash animation that is currently used in college physics online learning，is required to be migrated to mobile devices in order to meet the needs of using mobile devices for learning. HTML5( H5 for short) is currently the best substitution of Flash. Based on the design and development practice of H5 animation in the new physics textbooks，in this article，the design ideas and development steps of physics h5 animation is summarized，the two steps of topic selection and physical modeling and interface and interactive function design in detail with examples is described. Related Articles | Metrics

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One way to explain Ampere's circuital theorem GENG Zhi-hao College Physics    2021, 40 (7): 17-.   DOI: 10.16854 / j.cnki.1000-0712.200446 Abstract （464）      PDF（pc） （271KB）（322）       Knowledge map    Save A new distinct and concise method to demonstrate the Ampere’s circuital theorem is proposed for general physics course of non-physics majors.It is practibal to enhance students’comprehension of this theorem. Related Articles | Metrics

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Study of combining ideological and political education with Peer Instruction in college physics experiment CHEN Jun, ZHU Dao-yun, PANG Wei, WU Xiao, TANG Liang College Physics    2021, 40 (6): 57-.   DOI: 10.16854 /j.cnki.1000-0712.200371 Abstract （463）      PDF（pc） （835KB）（146）       Knowledge map    Save It is a difficult task to integrate ideological and political education into college physics experiment course because of the particularity of experimental teaching. In this paper，the ideological and political education combined with Peer Instruction method is applied to college physics experiment course innovatively. As a result，the students' interest and learning effect can be greatly enhanced by changing the traditional instillation teaching into autonomous discussion learning through this new teaching method. The core values of socialism run through the whole teaching naturally so as to achieve the goal of moistening things in silence. Related Articles | Metrics

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Classical and quantum statistical distributions of harmonic oscillators KANG Lin-hui, ZHANG Lin College Physics    2021, 40 (7): 30-.   DOI: 10.16854 / j.cnki.1000-0712.200508 Abstract （455）      PDF（pc） （359KB）（259）       Knowledge map    Save There are some differences and connections between classical statistics and quantum statistics，and they can be converted to each other under certain conditions. The harmonic oscillator model is very important in physics，for example，the movement of the harmonic oscillator state description，energy，and the uncertainty princi- ple，spatial distribution and probability distribution of the two kinds of statistical methods are compared and summa- rized，respectively. The classical statistics of harmonic oscillator and the similarities and differences with quantum statistical distribution are deepened to the further understanding of quantum dynamics behavior and cognition. Related Articles | Metrics

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Application of measurement uncertainty analysis in university physics experiments — gravity acceleration measured by single-swing ZHANG Zhu li, CHEN Xin lei, LU Mei hong College Physics    2022, 41 (2): 31-.   DOI: 10.16854/j.cnki.1000-0712.200521 Abstract （453）      PDF（pc） （826KB）（116）       Knowledge map    Save Gravity acceleration is an important mechanical constant in physics. There are many methods to measure the value of gravity acceleration, and the simple pendulum method is often used in university physics experiments. However, the experimental principle only studies the motion of the single pendulum ball and ignores the influence of the size of pendulum, buoyancy, cycloid mass and other factors, so the measurement results are not accurate enough. The relative accurate formula of gravity acceleration and the corresponding synthetic standard uncertainty formula are obtained by correcting the system error that caused in the measurement of gravity acceleration by the simple pendulum method. Finally, the measured data are analyzed and calculated reasonably, and the more accurate experimental results are obtained. Related Articles | Metrics

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Uniformity of magnetic field created by four parallel，coaxial and current-carrying square coils of equal size ZAN Hui-ping, ZHANG Yin-ke College Physics    2021, 40 (6): 14-.   DOI: 10.16854 / j.cnki.1000-0712.200373 Abstract （448）      PDF（pc） （2511KB）（84）       Knowledge map    Save Uniform magnetic field has many applications in scientific research and engineering technology. Based on Biot-Savart law and the superposition principle of magnetic field，the mathematical expressions of magnet- ic induction intensity created by four parallel，coaxial and current-carrying square coils of equal size ( FPCSCS) are derived. By using Taylor series expansion method，the conditions，under which the FPCSCS generates a mag- netic field of the best uniformity，have been found. The uniformity of magnetic fields produced by the FPCSCS in three cases is discussed. The results show that，in the optimum situation，the FPCSCS can generate a very homoge- nous magnetic field with magnitude relative deviation of less than 0.01% and direction deviation of less than 0.01 degree. Compared with the homogenous magnetic fields of square Helmholtz coil，the magnetic field of FPCSCS has obvious advantages，which are greater magnitude and better uniformity. Related Articles | Metrics

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Practices of teaching mode reform on“Computational Materials Science” ZHANG Peng College Physics    2021, 40 (6): 62-.   DOI: 10.16854 /j.cnki.1000-0712.210007 Abstract （440）      PDF（pc） （852KB）（60）       Knowledge map    Save An innovative country is based on innovative talents. How to realize this goal by a basic subject course? Herein，we propose a Practice -Theory -Innovation ( PTI) teaching model of professional curse. In this model，students do practices first to experience the applications of theory. Then，they will seek answers from theoretical study. When they come back to research，they will make innovative achievements. Thus，this model focus on not only the form and contents of classroom teaching，but also out-of-class research activities. Since 2017，the executing of PTI model has led to remarkable improvement，resulting in fourteen SCI papers of undegraduate students. It has been found that the student's innovation capacity can be improved by combining in-class lecturing and outof- class activities. Related Articles | Metrics

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Misunderstandings in the experiment of measuring acceleration of gravity with Kate 　　pendulum 　　——— Taking virtual simulation experiment as an example SHENG Yan College Physics    2021, 40 (10): 32-.   DOI: 10.16854 / j.cnki.1000-0712.210066 Abstract （439）      PDF（pc） （260KB）（143）       Knowledge map    Save Kate pendulum is an accurate and ingenious experimental method to measure the acceleration of gravity. In this paper，based on the principle，the model of Kate pendulum is introduced，the experimental method is summed up，some common experimental errors are pointed out，and the analysis is given so as to guide the ex- perimenters to pay attention to understand the experimental principles and avoids going into the experimental errors. Related Articles | Metrics

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Demonstration instrument for vacuum measurement WU Yuan, GUO Chao-xiu, YIN Ya-ling, CHEN Li-qing College Physics    2021, 40 (7): 38-.   DOI: 10.16854 / j.cnki.1000-0712.200380 Abstract （432）      PDF（pc） （293KB）（135）       Knowledge map    Save The difference between quantum mechanics and classical physics is that the energy of the vacuum is not zero. Normally，due to the small energy，it is hard to measure the vacuum field directly only when the quantum measurement，such as homodyne detection，is used. Meanwhile，there is a lack of the experimental demonstration based on quantum measurement in college physics，which makes the theory of quantum mechanics hard to be un- derstanded. In this paper，a demonstration instrument for vacuum measurement based on homodyne detection is pro- posed. This instrument is simple in principle，intuitive in phenomenon，easy to operate and maintain. It makes up for the blank of quantum mechanics experiment in college physics，which realizes the expansion of frontier physics in college physics teaching. Related Articles | Metrics

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How much charges on a hemisphere? QIU Wei-gang College Physics    2021, 40 (9): 21-.   DOI: 10.16854 / j.cnki.1000- 0712.200546 Abstract （431）      PDF（pc） （449KB）（227）       Knowledge map    Save The electric potential produced by two hemispheres with constant and opposite potential is expressed as infinite sums of Legendre functions in spherical coordinate. The electric charge density and total charges on the hemisphere are derived. Calculation shows that the charge is infinite. Related Articles | Metrics

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Electrostatic induction of the infinite ungrounded conductor plate FU Quan-hong, ZHENG Jian-bang, FAN Yuan-cheng, ZHANG Fu-li College Physics    2021, 40 (11): 5-.   DOI: 10.16854 / j.cnki.1000-0712.210041 Abstract （429）      PDF（pc） （239KB）（301）       Knowledge map    Save Utilizing the uniqueness theorem of the boundary value problem of electrostatic field，we strictly an- alyze the problem of electrostatic induction of the infinite ungrounded conductor plate，and use the simulation soft- ware of COMSOL Multiphysics to verify the theoretically calculated results. Related Articles | Metrics

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Quantum speed limit time XU Kai, ZHANG Guo-feng College Physics    2021, 40 (10): 1-.   DOI: 10.16854 / j.cnki.1000-0712.210015 Abstract （424）      PDF（pc） （174KB）（382）       Knowledge map    Save The minimum time required for the system to evolve from the initial state to the target state is defined as the quantum speed limit time. This concept can be used to estimate the maximum rate of evolution from a given quantum state to a desired target state. Here，the development of quantum speed limit time from closed system to open system is reviewed，and the influence of non-Markovian environment on the quantum speed limit time of open system is discussed. We hope that our review is helpful for the future study of the quantum speed limit time. Related Articles | Metrics

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Application of charge projection method in the study of charge distribution law of infinitely long conductor thin plate ZHOU Qun-yi¹, MO Yun-fei², ZHOU Li-li³, HOU Zhao-yang⁴ College Physics    2021, 40 (7): 19-.   DOI: 10.16854 /j.cnki.1000-0712.200545 Abstract （423）      PDF（pc） （596KB）（180）       Knowledge map    Save Using the charge distribution law of a uniformly charged cylinder of infinite length and the field strength formula of an infinitely long charged straight line，and adopting the charge projection method，the surface charge distribution of a charged conductor of finite width and infinite length has been deduced. According to the principle of electric potential superposition，the electric potential integral formula is derived; using the relationship between field strength and electric potential，the integral formula of the two components of electric field strength is derived. The formula is dimensionless，and the values of the components of electric potential and field strength are calculated through numerical integration. The electric potential and field strength of the charged conductor sheet of finite width and infinite length are shown in the picture，and the two-dimensional equipotential lines and electric field lines are also drawn in the diagram，which fully shows the distribution law of field strength. Related Articles | Metrics

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Superposition rule of refraction imaging of object points through multi-layer parallel 　　medium interface and several application analyses SHAO Yun College Physics    2021, 40 (8): 23-.   DOI: 10.16854 / j.cnki.1000-0712.200493 Abstract （423）      PDF（pc） （448KB）（70）       Knowledge map    Save In this paper，a simple and natural reasoning method is used to deduce the virtual image point posi- tion of the secondary refraction imaging of object point refracting through the parallel medium interface，and the so- called “superposition rule of refraction imaging of object points through multi-layer parallel medium interface”is found. This paper discusses the coordinates of image points in several special cases: the refraction phenomenon of “body head separation”of the female swimmer in swimming pool is analyzed and explained; the imaging character- istics of objects in the air through glass blocks are analyzed，the optical basis for people to usually use thin glass windows is pointed out; the refraction imaging of an object point in air through a medium with linear refractive index change is studied in detail，and it is pointed out that the position of the imaging point in the medium with uniformly varying refractive index is almost the same as that in the medium with uniform refractive index of same thickness， except for the large angle of view from 80° to 90°. The reasoning methods and conclusions in this paper may provide reference for the teaching and scientific research of related contents. Related Articles | Metrics

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Application of the formation mechanism of neutronstar to the education of solid state physics WANG Shuan-hu, TIAN Ying-yi, WANG Min, DAI Fu-ping College Physics    2021, 40 (6): 8-.   DOI: 10.16854 / j.cnki.1000-0712.200413 Abstract （416）      PDF（pc） （805KB）（167）       Knowledge map    Save Based on the discussion of dispersion relation and density of states in solid state physics，in this paper，the difference of the dispersion relation of electrons under relativistic and non-relativistic limit is studied.The difference eventually leads to a distinct final evolution results of supermassive celestial body. The process of theoretical calculation can be easily correlated to the study of electron behavior in solid state physics. Integrating this mechanism into the education of solid state physics can not only enhance the understanding on the electron be-havior in solid state matter，but also provide a deep insight to the relativistic behavior of electron. Related Articles | Metrics

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The intuitional teaching method of the beat phenomenon XIA Zheng-rong, LI Rong-qing, TONG Yue, XU Xiao-xue College Physics    2021, 40 (9): 10-.   DOI: 10.16854 / j.cnki.1000- 0712.200324 Abstract （416）      PDF（pc） （534KB）（176）       Knowledge map    Save Combining the rotating vector method， the constructed process of the beat phenomenon and the rea- son that caused the characteristic of the Beat phenomenon are analyzed. Then the amplitude and the phase position of the beat phenomenon are discussed in detail. Finally， the phase jump is also shown by the rotating vector method clearly. The method describing the beat phenomenon in this paper makes the model of the beat phenomenon so visu-al and intuitive that one can understand it very easily. Related Articles | Metrics

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Simple measurement of the axis distance and interpupillary distance ZHOU Si-ying¹, CHANG Kai-ge², MAO Sheng-chun², GAO Bo² College Physics    2021, 40 (12): 55-.   DOI: 10.16854 / j.cnki.1000-0712.210044 Abstract （415）      PDF（pc） （708KB）（67）       Knowledge map    Save If the interpupillary distance does not match the axis distance of one's glasses，the scene would be deformed，distorted and blurred，and this could result in visual fatigue and irreversible damage to the eyes. In this paper a measurement scheme by using laser pen，ruler and mobile phone is proposed. By analyzing the principle of optical imaging，the measurement models of axis distance in four position cases of laser pen are established，and the calculation formulas of two glasses with the same or the different degrees are given. Then a platform is built to do ex- periment，and the factors affecting on the accuracy are analyzed. Tracker video analysis software is also used to fur- ther reduce the measuring error. Finally，through taking pictures by using mobile phone，the interpupillary distance is accurately measured. Thus conveniently measuring the interpupillary distance and the axis distance and accurately judging whether they match or not are realized. Related Articles | Metrics