FLUCTUATIONS OF CASIMIR FORCES ON FINITE OBJECTS .2. FLAT CIRCULAR DISK

The zero-point fluctuations of a scalar field with Neumann boundary conditions are investigated on a flat circular disk. The Helmholtz equation is is separated in oblate spheroidal coordinates; the mean-square force acting perpendicularly on the disk is calculated by picturing the disk as an oblate spheroid with zero eccentricity. The force is averaged aver a time T, and the disk is taken small compared with cT. The results show that the fluctuations on a disk are roughly equal to those on a small sphere. For a one-sided disk divergences arise from the sharp edge, but the mean-square force has the same power dependence on T as for a hemisphere.