In \({\mathbb{R}}^ 2\), consider the strip \(y=0\), \(y=2a\) with a pair of U notches. The upper U notch is of the same size as the lower one and located symmetrically with respect to the line \(y=a\). The paper deals with the problem of finding a function in \({\mathbb{R}}^ 2\) which gives potential on the lower boundary as 1 and that on the upper boundary as - 1.
In an earlier paper [Q. Appl. Math. 41, 369-377 (1983; Zbl 0557.31002)] the author showed that the solution could be written as a linear combination of a set of harmonic functions up to additive linear terms. In this paper, he gives an alternate proof, deriving the set of harmonic functions from a single function (and not from an integral as earlier) and adjusting the boundary conditions on the curves without the use of conformal transformation. Some numerical examples are also given.