Electrode polarization effects have long aggravated the efforts of low frequency analysis, particularly those investigations carried out on biological material or in highly conductive media. Beginning from elementary equations of electrostatics and hydrodynamics, a comprehensive model is devised to account for the screening of a general planar electrode by an ionic double layer. The surface geometry of the planar electrode is left unspecified to include any type of micromachined array, Building on the previous work by DeLacey and White (1982, J. Chem. Sec. Faraday Trans. 2 78, 457) using a variational theorem, we extend their numerical results with compact analytic solutions, analogous to the Debye-Huckel potential for de systems, but applicable now to dynamic ac experiments. The variational approach generates functions that are not restricted by perturbation expansions or numerical convergence, representing optimal approximations to the exact solutions.