and of the total force are not identical, interpolation was used to determine the values of A$_{k}$ ( a ) at the separations corresponding to the total lateral force. After determination of the coefficients A$_{k}$ ( a ) from the fit, the signal S C lat was subtracted from the data for the total deflection signal S tot $_{lat}$. The obtained deflection signal S el lat now corresponds to the lateral electrostatic force The experimental force data in this equation were used to determine the calibration param- eter k$_{ben}$ and z$_{0}$ from the fit to the theoretical expression for the lateral electric force. To derive the analytic expression for the lateral electric force acting between the sinu- soidally corrugated surfaces of a sphere and a plate, we start with the electrostatic energy in sphere-plane configuration with smooth surfaces [47, 48] Here, the integration constant ˜ c is equal to [47] where 0 ≤ θ ≤ 1, and c$_{i}$ are defined in Eq. (2). Using the PFA, we obtain the electrostatic energy between sinusoidally corrugated sur- faces of a sphere and a plate in the form where z$_{s}$ − z$_{p}$ is given by Eqs. (3), (5) and (6). Using the definition of the lateral electric force [see the formula for the phase shift below Eq. (3)] and calculating all integrals in (17), we arrive at the result 15 F el $_{lat}$( a, ϕ ) = π $^{2}$ϵ$_{0}$ ( V − V$_{0}$ ) $^{2}$R A$_{1}$A$_{2}$ a $^{2}$Λ [ 2 √ 1 − β $^{2}$(1 + √ 1 − β $^{2}$) − 2 6 ∑ i =1 ic$_{i}$ ( a R ) i $^{+1}$Y$_{i}$ ] . (19) F el $_{lat}$( a, ϕ ) = − ∂ ∂x$_{0}$ E $^{el}$( a, ϕ ) = − 2 π Λ ∂ ∂ϕ E $^{el}$( a, ϕ ) (18) E $^{el}$( a, ϕ ) = 1 Λ ∫ Λ 0 dxE el , $^{sp}$( z$_{s}$ − z$_{p}$ ) , (17) ˜ c = 1 2 ln 2 + 23 40 + θ 126 , (16) E el , $^{sp}$( a ) = − 2 πϵ$_{0}$ ( V − V$_{0}$ ) $^{2}$R [ c$_{−}$$_{1}$ ln R a + ˜ c − 6 ∑ i =0 c$_{i}$ i + 1 ( a R ) i +1 ] . (15) F el $_{lat}$( a, ϕ ) = k$_{ben}$S el $_{lat}$( a, ϕ ) . (14)