Electrostatic field of a thin, unclosed spherical shell and a torus
Tóm tắt
The electrostatic problem for a thin, unclosed spherical shell and a torus is reduced to paired summation equations in the Legendre polynomials by means of formulas relating the spherical and toroidal harmonic functions. The paired equations are transformed to a Fredholm integral equation of the second kind. Formulas are obtained for computing the charges of the conductors in the form of a series in a small parameter. The capacitance is computed for certain geometrical parameters of the conductors.
Tài liệu tham khảo
Yu. Ya. Iossel’, É. S. Kochanov, and M. L. Strunskii, Calculating Electrical Capacitance (Énergoizdat, Leningrad, 1981), 288 pp.
V. P. Il’in, Numerical Methods of Solving the Problems of Electrical Physics (Nauka, Moscow, 1985), 336 pp.
E. Boridy, IEEE Trans. Electromagn. Compat. EMC-29, 131 (1987).
J. P. Chevailler, J. Electrost. 9, 307 (1981).
Ya. S. Uflyand, Zh. Tekh. Fiz. 48, 1741 (1978) [Sov. Phys. Tech. Phys. 23, 987 (1978)].
N. N. Lebedev, Special Functions and Their Applications (GITTL, Moscow, 1953), 380 pp.
V. Ya. Arsenin, Methods of Mathematical Physics and Special Functions (Nauka, Moscow, 1984), 384 pp.
Handbook of Special Functions, with Formulas, Graphs, and Mathematical Tables (Nauka, Moscow, 1984), 832 pp.
V. T. Erofeenko, Dif. Uravneniya 19, 1416 (1983).
Ya. S. Uflyand, Methods of Paired Equations in Problems of Mathematical Physics (Nauka, Leningrad, 1977), 220 pp.
A. F. Verlan’ and V. S. Sizikov, Integral Equations: Methods, Algorithms, and Programs (Naukova Dumka, Kiev, 1986), 732 pp.