A curious and useful theorem in two-dimensional electrostatics

American Journal of Physics

Volumn 67, Issue 2, 1999, Pages 107-115

  Jackson, J D ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033445078     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19203     Document Type: Article

References (19)

1. A. M. Thompson and D. G. Lampard, "A New Theorem in Electrostatics and its Application to Calculable Standards of Capacitance," Nature (London) 177, 888 (1956).
2. B. W. Petley, The Fundamental Physical Constants and the Frontier of Measurement (Hilger, Bristol, 1985), pp. 142-145.
3. N. M. Zimmerman, "A primer on electrical units in the Système International," Am. J. Phys. 66, 324-331 (1998).
4. D. G. Lampard, "A new theorem in electrostatics and its application to calculable standards of capacitance," Proc. IEEE 104C, 271-280 (1957).
5. L. J. van der Pauw, "A method of measuring specific resistivity and Hall effect of discs of arbitrary shape," Philips Res. Rep. 13, 1-9 (1958).
6. D. G. Lampard and R. D. Cutkosky, "Some results on the cross-capacitances per unit length of cylindrical three-terminal capacitors with thin dielectric films on their electrodes," Proc. IEEE 107C, 112-119 (1960).
7. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998), 3rd ed., p. 39.
8. See, for example, Ref. 7, p. 89, Problem 2.15.
9. E. T. Whittaker and G. N. Watson, A Course in Modern Analysis (Cambridge U. P., Cambridge, 1952), 4th ed., reprinted, Chap. XXI.
10. It turns out that string theorists make use of Jacobi's elliptic and theta functions. Consult your local string person for details.
11. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), 4th ed., p. 924, formula 8.197.4.
12. -4π+⋯]. The third term here disagrees with Lampard's Eq. (43) - Ref. 4. He has a coefficient - 10 instead of +6.
13. E. T. Copson, Theory of Functions of a Complex Variable (Oxford U.P., Oxford, 1935), reprinted 1955, pp. 185-187.
14. C. E. Pearson, Handbook of Applied Mathematics (Van Nostrand, New York, 1983), pp. 261-263.
15. See, for example, Ref. 7, pp. 38-40.
16. See Ref. 7, pp. 37, 38.
17. H. Kober, Dictionary of Conformal Representations (Dover, New York, 1957), 2nd ed., p. 182.
18. See Ref. 7, p. 89, Problem 2.12.
19. R. D. Cutkosky, "New NBS measurements of the absolute farad and ohm," IEEE Trans Instrum. Meas. IM-23, 305-309 (1974).