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    20 September 2020 Volume 39 Issue 9
      
    Research on blended learning strategies ———taking the teaching during COVID-19 quarantine period as an example
    WANG Zu-yuan, ZHANG Rui, ZHANG Zhi-hua
    College Physics. 2020, 39(9):  1-5.  doi:10.16854 /j.cnki.1000-0712.200162
    Abstract ( 1568 )   PDF (921KB) ( 807 )  
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    Based on the experience on blended learning of University Physics and the observation of teaching

    activity during COVID-19 quarantine period，the characteristics and the learning achievement of blended learning

    in different modes are analyzed. The common problems in online learning and blended learning are discussed，and

    some suggestions on blended learning in COVID-19 quarantine period are also presented.

    A brief analysis of different form of Pauli-Fierz Hamiltonian in non-relativistic limit
    ZHANG Jun, ZHU Zhan-wu, HE Ze-dong
    College Physics. 2020, 39(9):  6-8.  doi:10.16854 /j.cnki.1000-0712.190536
    Abstract ( 1492 )   PDF (213KB) ( 608 )  
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    When we discuss the interaction of atoms or molecules with quantized electromagnetic waves ( photons) ，the Hamiltonian in length gauge takes the advantage by replacing the vector potential A by electric filed multiplying the dipole. However，formulas in different papers seem to have different forms. In this paper，we start from Pauli-Fierz Hamiltonian in velocity gauge and obtain the length gauge Hamiltonian in coordinate and momentum 　representation，respectively，which proves the equivalence between different forms. We hope this could help students to understand the Hamiltonian in different forms.
    An analysis of the key points of wave problems in College Physics
    LI Jun, QIAN Cheng-yi, MA Mo-nan, YUAN Cheng-xun, MENG Qing-xin,
    College Physics. 2020, 39(9):  9-16.  doi:10.16854 /j.cnki.1000-0712.190550
    Abstract ( 1994 )   PDF (3134KB) ( 525 )  
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    The wave constitutes an indispensable part in College Physics. It is not only the extension of electromagnetic wave，but also the basis of optics and quantum mechanics. Students need to work hard on wave problems. In this paper，by investigating the students in Harbin Institute of Technology，four key points in wave problem are put forward，the key elements are analyzed，and some solutions are provided to help the students to understand 　these key points.
    Proof of the relationship between the shape of the spherical droplet surface and the principle of free energy minimization
    JIN Kang, WANG Xin-yi, GUI Kai-hang
    College Physics. 2020, 39(9):  17-22.  doi:10.16854 /j.cnki.1000-0712.190512
    Abstract ( 1207 )   PDF (1375KB) ( 596 )  
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    The surface shape of the droplets in the vacuum is determined by the principle of surface free energy minimization. In the case of ignoring droplet gravity，the minimum free energy corresponds to the minimum surfacearea of the droplet. We derive the equations satisfied by the minimum surface under fixed volume constraints，and use the linearized iterative method to numerically solve the equation to prove that the surface is spherical. In addition，we prove that if the final thickness of the super-spreading liquid film is constant，the liquid film spreading shape is also determined by the principle of minimum free energy，and its shape is circular.
    Physical distribution mechanism of the power supply
    YIN Hai-feng, ZENG Chun-hua
    College Physics. 2020, 39(9):  23-26.  doi:10.16854 /j.cnki.1000-0712.190415
    Abstract ( 1032 )   PDF (461KB) ( 516 )  
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    This paper mainly analyses a linear circuit with two power sources. There are three types of this circuit: the current - controlled dual - port network，voltage - controlled dual - port network and hybrid dual - port network. A dual-port network VCR can be obtained by measuring and other methods. The physical distribution of each part of the power of two power sources can be obtained when the VCR of two-port network is known. The power of each power supply consists of two parts. One part is equal to the power provided by the power supply when it is connected to the circuit separately. Another part is the increased power due to the interaction between the two power sources when they are both connected to the circuit. The increased power depends on two power sources and circuit parameters. According to the reciprocity theorem，when there is no controlled source，for current-controlled twoport networks and voltage-controlled two-port networks，the increased power of each power source due to interaction

    is equal. That is to say，the increased loss power of the circuit is shared equally by the two power sources. For a hybrid dual-port network，when there is no controlled source，the increased absorption power of one power source is equal to the increased supply power of another power source due to the interaction. The sum of the power of both power supplies is equal to the sum of the power of both power supplies when it is connected to the circuit separately. In this case，the effect of interaction is that one power source charges another power source. The results of this study are universal. It can help one to solve the power source problem of power grid，and can also solve the power source problem of other electronic circuits.

    Agrange density，motion equation and continuous equation of relativistic fluid
    LIANG Gui-xiong
    College Physics. 2020, 39(9):  27-30.  doi:10.16854 /j.cnki.1000-0712.190307
    Abstract ( 1759 )   PDF (174KB) ( 441 )  
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    Under reasonable assumptions，this paper presents a Lagrangian density of relativistic fluid from the energy-momentum tensor of the relativistic fluid，and presents the equation of motion for relativistic fluid based on the Lagrangian density and the principle of least action. In the limit of low speed and low pressure our equations of motion reduces to Navier-Stokes equations. The continuity equation of fluid is also discussed. It is found that the continuity equation of fluid in Newtonian mechanics can be established only when the influence of pressure and external force can be neglected，even at the low speed of flat space-time.
    Infinite sum and residue theorem
    QIU Wei-gang
    College Physics. 2020, 39(9):  31-33.  doi:10.16854 /j.cnki.1000-0712.190431
    Abstract ( 1598 )   PDF (146KB) ( 656 )  
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    The contour integral of a complex function on an infinite square is approximately the same as another

    complex function. The analytical expression of infinite summation of all the zeroes of some transcendental equation is

    derived by residue theorem，which is verified by the numerical calculation.

    High-frequency resistance of metal and the method of its measurement and correction
    ZHOU Rong-hao, YANG Yong, ZHANG Qing, TIAN Fa-bao
    College Physics. 2020, 39(9):  34-40.  doi:10.16854 /j.cnki.1000-0712.200001
    Abstract ( 1140 )   PDF (1065KB) ( 585 )  
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    Resistance is an important physical parameter of metal materials. The measurement of high-frequencyresistance is affected by the skin effect， the distributed inductance and the capacitance. Rare special experimental measurement is reported about it. In this paper， in the condition that the test objects can be actively changed and the metal filaments are used for the experimental measurement， the high-frequency resistance measurement can better suppress the skin effect. Meanwhile，by analyzing the resistance， inductance and capacitance equivalent circuits of the fixed-shape non-ferromagnetic metal filament samples， the vector voltage analysis data is obtained by a frequency-sweeping phase-locked amplifier. The method of optimal matching is used to successfully modify the influence of the high -frequency distributed inductance and capacitance on the high -frequency resistance measurement of metals from the perspective of engineering practice. An improved method for high - frequency resistance measurement of ferromagnetic metals is also proposed. The electrical conductivity of the metal remained unchanged at high frequency，which is consistent with the theoretical analysis results. This study provides measurement ideas for higher frequency resistance，and has also significance for improving electromagnetic nondestructive testing and electromagnetic compatibility research and design.
    Study on the phenomenon of star-burst
    WANG Ying, ZHOU Yu-han, XIA Wang-suo
    College Physics. 2020, 39(9):  41-46.  doi:10.16854 /j.cnki.1000-0712.190476
    Abstract ( 1891 )   PDF (1618KB) ( 627 )  
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    In this paper， the interesting phenomenon of star-burst ( which arose from the pictures taken from bulbs at night) is investigated theoretically and experimentally. Through properly simplifying the physical model of photographing process， the star-burst is analyzed theoretically depending on Francophile diffraction theory，with the influencing factors including the aperture shape，aperture size， incident wavelength and camera distance，etc. Then the influencing factors for star-burst has been systematically studied through contrast experiments. Further comparison on the results got from theoretical and experimental methods has been methodically carried out. Finally，advice for how to obtain obvious star-burst is given.
    Some thoughts regarding physics experimental courses at medical college based on student-centered teaching
    LI Hui, WANG Chun-feng, SUN Da-gong, KA Wei-bo, YUAN Gui-hong, ZHANG Si-qing, GAO Song
    College Physics. 2020, 39(9):  47-50.  doi:10.16854 /j.cnki.1000-0712.190573
    Abstract ( 1047 )   PDF (413KB) ( 286 )  
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    Teaching reform in regards to teaching content and method has been conducted for physics experiment course in the Peking University Health Science Center for more than ten years. The fundamental physics，medical application and modern technologyare emphasized in physics experiment course. A deep investigation for the student !s opinion on the physics experiment course is also carried out. A comprehensive thoughts are presented

    with regard to the results of the investigation.The results obtained in this study should provide reference for future teaching reform.

    Mean relative speed between different molecules in mixed gases
    HAI Wen-long, PANG Dan-yang,
    College Physics. 2020, 39(9):  51-52.  doi:10.16854 /j.cnki.1000-0712.200041
    Abstract ( 1532 )   PDF (152KB) ( 376 )  
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    Based on the definition of the relative speed， the mean relative speed between different molecules in mixed gasses is derived by the combination of Maxwell speed and velocity distributions.
    Theoretical calculation and experiment of linear expansion coefficient of metal
    LIU Jin, ZHANG Meng, LUO Duan-bin
    College Physics. 2020, 39(9):  53-58.  doi:10.16854 /j.cnki.1000-0712.200085
    Abstract ( 1653 )   PDF (867KB) ( 446 )  
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    In this paper，the coefficient of thermal expansion of aluminum and copper metals is obtained by calculating the lattice constants，binding energy and Debye temperature via the density functional method based on quantum mechanics. Experimental design and data measurement are also carried out. Moreover，the theoretical simulation values are compared with the experimental results achieved by using an optical lever. The error sources were analyzed and the experimental methods for improving the errors were proposed. The results should provide reference for the future experimental design and theoretical simulation of metal thermal expansion coefficient in university physics courses.
    Research on using mirror image method to solve the electric field of spherical projection on the plane
    ZHAN Yan, LIU Jin, CHANG Yue-yue, WANG Wen-jing, ZHANG Xian-mei
    College Physics. 2020, 39(9):  59-65.  doi:10.16854 /j.cnki.1000-0712.200019
    Abstract ( 1619 )   PDF (2280KB) ( 471 )  
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    The mirror image method can be used to solve the electrostatic field in the system with high symmetry. This paper discusses a model in which there is a circular projection on the plane of an infinite grounded conductor， and the point charge is located on the axis of symmetry of the system and has no contact with the surface of the conductor. Through the discussion on the relations among the radius of the circle，the distance between the center of the circle and the plane，and the shortest distance between the charge and the dome，three convergent models are summarized. In the first two cases，no matter where the point charge is，a stable solution can always be obtained， and the spatial electric field distribution is given by combining with MATLAB simulation. The latter case cannot be solved by the mirror image method，which reflects the limitations of the mirror image method.
    Symmetry of electromagnetic field，magnetic charge and magnetic monopole: An example of symmetry analysis in teaching collage electrodynamics
    YUAN Ming-yue, LI Tong, HUANG Xiao-yan, LIN Fang, ZHANG Zhi-you,
    College Physics. 2020, 39(9):  66-71.  doi:10.16854 /j.cnki.1000-0712.190486
    Abstract ( 1506 )   PDF (320KB) ( 778 )  
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    Symmetry plays great importance role in modern physics. The symmetry analysis in electrodynamics is not only useful for solving specific excises，but can also provide us profound understanding of basic concepts.In this paper，we briefly summarize the general symmetry properties of electromagnetic fields in its non-relativity form. We address that gauge invariance is the fundamental symmetry classic electromagnetic field and governs the electromagnetic interaction. The broken of duality in electromagnetic field is an example of this governance. Based on these understanding，two confusing concepts，that magnetic charge and magnetic monopole，are further discussed.
    Simulation and visualization of electrostatic field and electric charge movement based on Vpython
    WANG Yao, LIU Yu-ying, ZHU Shi-qiu
    College Physics. 2020, 39(9):  72-77.  doi:10.16854 /j.cnki.1000-0712.190463
    Abstract ( 1611 )   PDF (1475KB) ( 1042 )  
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    Based on Coulomb’s law and superposition principle of electric field，this paper explores the electrostatic field of point charge and charge system. With the help of computer software VPython，the electrostatic field under various charge distributions is simulated. Data analysis is carried out by Plotly software. In addition，we study the trajectory and energy characteristics of charged particles in the electrostatic field. Also，we visualize electric dipole’s three-dimensionalmotion in the electrostatic field in real-time. Teaching practice indicated that: thesimulating and visualizing electrostatic field and charge movement based on VPython andPlotlyenables students to have a better understanding of electrostatics-related knowledge，which is a useful supplement to the classic physics teaching.

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