Image charges from boundary value problems




Method of images, Laplace's equation, generating functions


The examples usually solved by means of the method of images are revisited solving directly the Laplace equation. We also give a simple derivation of the axially symmetric solutions of the Laplace equation in spherical coordinates and of the translationally symmetric solutions of the Laplace equation in cylindrical coordinates.


L. Eyges, The Classical Electromagnetic Field (AddisonWesley, Reading, Mass., 1972, reprinted by Dover, New York, 1980). Sec. 4.4.

J.R. Reitz, F.J. Milford, and R.W. Christy, Foundations of Electromagnetic Theory, 4th ed. (Addison-Wesley, Reading, Mass., 1979). Chap. 3.

R.K. Wangsness, Electromagnetic Fields, 2nd ed. (Wiley, New York, 1986). Sec. 11-2.

P. Lorrain, D.R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (Freeman, New York, 1988). Sec. 11.2.

J.D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998). Chap. 2.

D.J. Griffiths, Introduction to Electrodynamics, 4th ed. (Pearson, Boston, 2013). Sec. 3.2.

A. Zangwill, Modern Electrodynamics (Cambridge University Press, Cambridge, 2013). Sec. 8.3.

T. Matsushita, Electricity and Magnetism (Springer, Tokyo, 2014). Sec. 2.2.

F. Lacava, Classical Electrodynamics, From Image Charges to the Photon Mass and Magnetic Monopoles (Springer, 2016). Chap. 3.

L. Eyges, op. cit., Sec. 4.5.

A. Zangwill, op. cit., Sec. 8.3.2.

R.K. Wangsness, op. cit., Sec. 8-1.

A. Zangwill, op. cit., Sec. 4.5.1.

L. Eyges, op. cit., Sec. 3.4.

L. Eyges, op. cit., Eq. (3.48).




How to Cite

G. F. Torres del Castillo, “Image charges from boundary value problems”, Rev. Mex. Fis. E, vol. 20, no. 2 Jul-Dec, pp. 020213 1–, Jul. 2023.