ABSTRACT
The interior of a conducting sphere, and the interiors of conducting cylinders, truncated at both ends by conducting sheets, are examples of conducting cavities—finite regions within which electric fields are contained. We turn from these quantitative uses of (25.57) to its qualitative side. An outward displacement of the boundary of a cavity decreases the eigenvalue of any mode. If the given region can be transformed in this way into another one, with known properties, and a desired mode identified among those of the modified region, the latter eigenvalue provides a lower bound to the eigenvalue of interest.
