关键词: 格林互易定理, 静电学, 电势, 拉马努金无限求和公式

Abstract: Green’s reciprocation theorem is refereed as to a mathematical relationship between the potentials of any two groups of conductors with electrostatic balance under different charge distributions. Such a relationship stands under any conductor shapes and any other conductor distributions. In this work, we discuss the application of Green’s reciprocation theorem in electrostatics and checking priori mathematical identities. By comparing with the method of images and the method of eigenfunction expansion, we show the advantages of Green’s reciprocation theorem in dealing with some electrostatic problems. In addition, this work lists the infinite parallel plate capacitor problems which can be easily solved by Green’s reciprocation theorem, but hardly be solved by the traditional methods. In particular, this work designs an ideal experimental protocol to test the famous Ramanujan mathematical formula and some other mathematical identities based on Green’s reciprocation theorem.

Key words: Green’s reciprocation theorem, electrostatics, electric potential, Ramanujan formula