On the force between a dielectric cylinder in a constant electric field and a conducting half space

The force between an infinitely long dielectric cylinder in a constant electric field and a conducting half space is determined using the separation of variables technique on the Laplace equation in bipolar coordinates. The force is obtained as a series containing the relative distance between the cylinder and the half space as a parameter. This series is not uniformly convergent for the cylinder approaching the half space and the corresponding force cannot be obtained by performing the limit term per term. A special asymptotic analysis is presented leading to an analytic expression for this limiting value of the force.