%0 Journal Article %J Proceedings of the National Academy of Sciences %D 2011 %T Casimir force between sharp-shaped conductors %A Mohammad F. Maghrebi %A Sahand Jamal Rahi %A Thorsten Emig %A Noah Graham %A Robert L. Jaffe %A Mehran Kardar %X Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. %B Proceedings of the National Academy of Sciences %V 108 %P 6867 - 6871 %8 2011/04/11 %G eng %U http://arxiv.org/abs/1010.3223v1 %N 17 %! Proceedings of the National Academy of Sciences %R 10.1073/pnas.1018079108