Regularization of self inductance

TL;DR

This paper presents methods to regularize divergent integrals in calculating the self-inductance of a single loop, extending the mutual inductance formula to the case of identical loops.

Contribution

It introduces novel regularization techniques for self-inductance calculations using the Neumann formula, addressing divergence issues.

Findings

Regularization methods successfully define self-inductance.

Extension of mutual inductance formula to identical loops.

Addresses divergence in self-inductance integrals.

Abstract

We introduce several methods to define the self-inductance of a single loop as the regularization of divergent integrals which we obtain by applying Neumann (or Weber) formula for the mutual inductance of a pair of loops to the case when two loops are identical.