  A periodic homogenization model of the electrostatic equation is constructed
for a comb drive with a large number of fingers and whose mode of operation is
in-plane and longitudinal. The model is obtained in the case where the distance
between the rotor and the stator is of an order $\varepsilon ^{\alpha }$,
$\alpha \geq 2$, where $\varepsilon$ denotes the period of distribution of the
fingers. The model derivation uses the two-scale convergence technique.\ Strong
convergences are also established. This allows us to find, after a proper
scaling, the limit of the electrostatic force applied to the rotor in the
longitudinal direction.
