We show that the field of a charge at rest can always be considered as a superposition of evanescent waves of zero frequency. By proposing a two-dimensional Fourier expansion (instead of the three-dimensional one imposed by Landau and Lifshitz), we obtain a development of the Coulomb field in plane evanescent waves of zero frequency. This development is not valid in an arbitrary plane that contains the charge. By proposing a one-dimensional Fourier expansion we obtain a development in cylindrical evanescent waves of zero frequency. This last development is not valid in an arbitrary axis that contains the charge. These expansions enable us to analyze electrostatic boundary-value problems in a novel way.
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