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APPLICATIONS OF GREEN'S FUNCTIONS IN CALCULATING THE MUTUAL CAPACITANCE BETWEEN SMALL BODIES

APPLICATIONS OF GREEN'S FUNCTIONS IN CALCULATING THE MUTUAL CAPACITANCE BETWEEN SMALL BODIES

LIN WEI-GANG
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• Abstract

In industry and in laboratory work oftentimes we are confronted with the problem of electromagnetic shielding between two bodies. In many ceases it is sufficient to have electrostatic shielding, and thus the interaction between two bodies can be determined by examining the mutual capacitance between them. When the interfering body is small and can be considered as a point source, its effect in the presence of another grounded conductor (in our case, the metallic shield) can be calculated by means of the Green's function for this grounded conductor surface. As the Green's functions for various surfaces are well established so these various forms of shielding can be handled by the method proposed in this paper.Green's functions for regions bounded by surfaces of oblate spheroidal as well as prolate spheroidal coordinate system are discussed with a mind to supplement a few formulas for the Legendre function with imaginary variables which are useful in physical and technical problems and which do not seem to appear in popular literatures.The problem of a hole of arbitrary shape on a conducting surface is then discussed with emphasis on the allowable size of the hole on a conducting surface of finite dimension, verifying the experimental results in literature. Finally the formula for calculating the mutual capacitance of two small bodies, one of which is enclosed by a closed metallic shield with a hole on its surface is given.

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Cited By

•  [1]
•  [1] Zhao Yun-Jin, Tian Meng, Huang Yong-Gang, Wang Xiao-Yun, Yang Hong, Mi Xian-Wu. Renormalization of photon dyadic Green function by finite element method and its applications in the study of spontaneous emission rate and energy level shift. Acta Physica Sinica, 2018, 67(19): 193102. doi: 10.7498/aps.67.20180898 [2] HU NING. THE DERIVATION OF ONE-PARTICAL GREEN'S FUNCTION BY THE METHOD OF DISPERSION RELATION. Acta Physica Sinica, 1962, 79(10): 509-513. doi: 10.7498/aps.18.509 [3] Guo Ru-Hai, Shi Hong-Yan, Sun Xiu-Dong. The calculation of strain distribution in quantum dots with Green method. Acta Physica Sinica, 2004, 53(10): 3487-3492. doi: 10.7498/aps.53.3487 [4] XU HONG-HUA. THE INTERACTION PICTURE IN THE CLOSED TIME PATH GREEN'S FUNCTIONS. Acta Physica Sinica, 1985, 34(10): 1359-1362. doi: 10.7498/aps.34.1359 [5] Ding Yao-Gen, Zhao Ding, Sun Peng, Wang Jin-Hua. Application of dynamic track method in output-section calculation of klystrons. Acta Physica Sinica, 2006, 55(5): 2389-2396. doi: 10.7498/aps.55.2389 [6] Zhao Da-Zun, Zhang Hai-Tao, Gong Ma-Li, Wang Dong-Sheng, Li Wei. Applications of group theory to calculations of photonic band gap. Acta Physica Sinica, 2004, 53(7): 2060-2064. doi: 10.7498/aps.53.2060 [7] YANG ZHENG-JU. THE ELASTIC GREEN'S FUNCTION OF ANISOTROPIC CUBIC CRYSTALS AND ITS APPLICATIONS. Acta Physica Sinica, 1987, 36(5): 599-612. doi: 10.7498/aps.36.599 [8] XU ZHI-HUA, FAN HONG-YI. RELATIONSHIP BETWEEN LATTICE GREEN'S FUNCTIONS FOR THE SEMI-INFINITE AND THE INFINITE SQUARE LATTICES AND ITS APPLICATION. Acta Physica Sinica, 1996, 45(8): 1372-1379. doi: 10.7498/aps.45.1372 [9] CHENG CHIN-CHI, PU FU-CHO. APPLICATION OF THE GREEN'S FUNCTION METHOD TO THE THEORY OF ANTIFERROMAGNETISM FOR S≥1/2. Acta Physica Sinica, 1964, 111(7): 624-635. doi: 10.7498/aps.20.624 [10] ZHANG LI-YUAN. GREEN'S FUNCTION METHOD FOR ENERGY BAND CALCULATIONS IN THE SCALAR RELATIVISTIC APPROXIMATION (SRA-KKR). Acta Physica Sinica, 1981, 30(8): 1122-1126. doi: 10.7498/aps.30.1122 [11] LIN WEI-GUAN. APPLICATION OF THE APPROXIMATE EVALUATION OF BESSEL FUNCTIONS TO FREQUENCY MODULATION SYSTEM. Acta Physica Sinica, 1955, 31(5): 411-420. doi: 10.7498/aps.11.411 [12] Lei Xiao-Li, Wang Da-Wei, Liang Shi-Xiong, Wu Zhao-Xin. Wavefunction and Fourier coefficients of excitons in quantum wells: computation and application. Acta Physica Sinica, 2012, 61(5): 057803. doi: 10.7498/aps.61.057803 [13] Zhang Hui-Yun, Liu Meng, Yin Yi-Heng, Wu Zhi-Xin, Shen Duan-Long, Zhang Yu-Ping. Study on scattering properties of the metal wire gating in a THz band based on Green function method. Acta Physica Sinica, 2013, 62(19): 194207. doi: 10.7498/aps.62.194207 [14] Wu Hao, Zhu Tuo, Kong Yan, Chen Wei, Yang Jian-Lei. Application of fluorescence spectra based on radial basis function neural network in identification of bacteria. Acta Physica Sinica, 2010, 59(4): 2396-2400. doi: 10.7498/aps.59.2396 [15] HE YU-SHENG. THE TWO WINDOW FOURIER TRANSFORM TECHNIQUE AND ITS APPLICATION IN THE SPECTRUM ANALYSIS OF QUANTUM OSCILLATIONS. Acta Physica Sinica, 1986, 35(4): 443-450. doi: 10.7498/aps.35.443 [16] Xu Shi-Min, Xu Xing-Lei, Li Hong-Qi, Wang Ji-Suo. Differential quotient rules of operator in composite function and its applications in quantum physics. Acta Physica Sinica, 2014, 63(24): 240302. doi: 10.7498/aps.63.240302 [17] LIU SHI-KUO, ZHAO QIANG, FU ZUN-TAO, LIU SHI-DA. EXPANSION METHOD ABOUT THE JACOBI ELLIPTIC FUNCTION ANDITS APPLICATIONS TO NONLINEAR WAVE EQUATIONS. Acta Physica Sinica, 2001, 50(11): 2068-2073. doi: 10.7498/aps.50.2068 [18] Chen Xiao-Bin, Duan Wen-Hui. Quantum thermal transport and spin thermoelectrics in low-dimensional nano systems: application of nonequilibrium Green's function method. Acta Physica Sinica, 2015, 64(18): 186302. doi: 10.7498/aps.64.186302 [19] Zhang Zhong-hua. PERTURBATION METHOD FOR VARIABLE BOUNDARY PROBLEMS AND APPLICATION TO THE EVALUATION OF ERRORS IN PRECISE CAPACITORS. Acta Physica Sinica, 1979, 1656(4): 563-570. [20] Gao Xin, Yin Hong-Xia, Liu Bo, Luo Shu-Qian, Gao Xiu-Lai, Zhu Pei-Ping, Wang Jun-Yue, Yuan Qing-Xi, Huang Wan-Xia, Wu Zi-Yu, Fang Shou-Xian, Shu Hang. Diffraction enhanced imaging computer tomography. Acta Physica Sinica, 2006, 55(3): 1099-1106. doi: 10.7498/aps.55.1099
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• Received Date:  02 June 1958
• Published Online:  20 January 1959

APPLICATIONS OF GREEN'S FUNCTIONS IN CALCULATING THE MUTUAL CAPACITANCE BETWEEN SMALL BODIES

• 1. 成都电讯工程学院

Abstract: In industry and in laboratory work oftentimes we are confronted with the problem of electromagnetic shielding between two bodies. In many ceases it is sufficient to have electrostatic shielding, and thus the interaction between two bodies can be determined by examining the mutual capacitance between them. When the interfering body is small and can be considered as a point source, its effect in the presence of another grounded conductor (in our case, the metallic shield) can be calculated by means of the Green's function for this grounded conductor surface. As the Green's functions for various surfaces are well established so these various forms of shielding can be handled by the method proposed in this paper.Green's functions for regions bounded by surfaces of oblate spheroidal as well as prolate spheroidal coordinate system are discussed with a mind to supplement a few formulas for the Legendre function with imaginary variables which are useful in physical and technical problems and which do not seem to appear in popular literatures.The problem of a hole of arbitrary shape on a conducting surface is then discussed with emphasis on the allowable size of the hole on a conducting surface of finite dimension, verifying the experimental results in literature. Finally the formula for calculating the mutual capacitance of two small bodies, one of which is enclosed by a closed metallic shield with a hole on its surface is given.

Reference (1)

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