Abstract
The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, and , and the cylinder’s parabolic radius . As , the proximity force approximation becomes exact. The opposite limit of corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.
- Received 24 October 2009
DOI:https://doi.org/10.1103/PhysRevD.81.061701
©2010 American Physical Society