found to be 46 times larger than the bending spring constant K$_{ben}$ (see the next section). Because of this the normal Casimir force could lead to only a negligible change in the position of the second sphere and in the phase of the corrugations. Thus the setup used is much more sensitive to detecting the lateral Casimir force, while simultaneously suppressing the effect of the normal Casimir force. The calibration of the cantilever (i.e., the determination of its spring constants), the measurement of the residual potential difference V$_{0}$ between the sphere and the plate, and the determination of the separation on contact z$_{0}$ were done by using both the normal and lateral electric forces. We begin with the determination of K$_{tor}$ and V$_{0}$ by means of the normal electric force. For this purpose we have measured the torsional cantilever deflection due to the voltages V applied to the grating while the sphere remained grounded. This was performed through the measurement of the difference signal between the bicell photodiodes shown in Fig. 1. To determine the parameters of our interest, the measured deflection signal S el nor at some separation a between the zero levels of corrugations on the grating and on the sphere, where the Casimir force is negligible, should be fitted to the theoretical expression for the normal electrostatic force between the corrugated surfaces. To attain these ends we begin with a brief derivation of such an expression in the sphere-plate configuration which is not available in the literature. In the configuration of an ideal metal sphere above an ideal metal plate with smooth boundary surfaces the exact expression for the electric force is well known [44]. In the range of separations from a = 100 nm to a = 6 µ m it can be represented [45] by the following polynomial with a relative error less than 10 − $^{4}$% where ϵ$_{0}$ is the permittivity of free space and the numerical coefficients c$_{i}$ are given by 10 c$_{−}$$_{1}$ = 0 . 5 , c$_{0}$ = − 1 . 18260 , c$_{1}$ = 22 . 2375 , c$_{2}$ = − 571 . 366 , c$_{3}$ = 9592 . 45 , c$_{4}$ = − 90200 . 5 , c$_{5}$ = 383084 ., c$_{6}$ = − 300357 . (2) F el , sp nor ( a ) = − 2 πϵ$_{0}$ ( V − V$_{0}$ ) $^{2}$Φ( a ) , Φ( a ) = 6 ∑ i = − 1 c$_{i}$ ( a R ) i , (1) III. ELECTROSTATIC CALIBRATIONS