Concerning the electrical interaction of circular holes in a plane conducting screen

The potential problem of two nearby holes in an infinitely thin perfectly c onducting screen immersed in a homogeneous normal electrostatic field is co nsidered. Expressions are derived for the double layer of charge arising in the plane of the hole, the centre of gravity of this distribution and the total amount of polarization induced by a nearby point dipole. In the deriv ation a set of integrals are used that connect the terms of a series expans ion of the potential in the oblate spheroidal system of co-ordinates with s ources on the focal disk. The results are applied to solve the excess polar ization and centre of the dipole distributions for two similar as well as t wo dissimilar holes.