We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing pote
ntial upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurement performed in the parallel plane configuration, showing that the dependence on distance of the minimizing potential, if present at all, is milder than in the sphere-plane or cylinder-plane geometries. General considerations on the interplay between the distance-dependent minimizing potential and the precision of Casimir force measurements in the range relevant to detect the thermal corrections for all geometries are finally reported.
We derive exact expressions for the Casimir scalar interaction energy between media-separated eccentric dielectric cylinders and for the media-separated cylinder-plane geometry using a mode-summation approach. Similarly to the electromagnetic Casimir
-Lifshitz interaction energy between fluid-separated planar plates, the force between cylinders is attractive or repulsive depending on the relative values of the permittivities of the three intervening media.
