A slender dielectric body embedded in an arbitrary external potential (Q2716588)

The author considers the problem of a slender dielectric body in an electrostatic field. He shows that the evaluation of the fields within and without the body is equivalent to the determination of the polarization surface charge density \(q\). He considers the Fredholm boundary integral equation for \(q_2\) and asymptotically expands and inverts it. If \(\partial= E_2/E_1\) where \(E_1\) and \(E_2\) are the dielectric constants inside and outside the body respectively, approximate solutions are provided for the three cases \(\partial- 1\geq O(1)\), \(\partial= O(1)\) and \(1-\partial= O(1)\). As an example, the author considers the particular case of a slender dielectric ellipsoid where the exact solution can be obtained.