The potential of infinite arrays of electrostatic dipoles

The characteristics of infinite arrays of equal electrostatic dipoles, which are useful as the limiting cases of finite dipole arrays, are studied. The most important characteristic is the potential of the array, which is obtained by summing the potentials of hundreds, thousands, or even more dipoles to find the result for an infinite array. Linear dipole arrays are considered first, and four examples are presented, with the direction of the dipoles taken first as perpendicular and then parallel to the plane of the array. In addition, dipoles were taken in one direction and than in alternately opposite directions. Similar results for several plane-surface arrays are presented with various dipole directions specified.<>