Mutual Inductance Calculation Between Circular Filaments Arbitrarily Positioned in Space: Alternative to Grover´s Formula

In this paper, we present the full derivation of a new formula for calculating the mutual inductance between inclined circular filaments arbitrarily positioned with respect to each other. Although such a formula was already proposed by Grover more than 50 years ago, the formula presented here is slightly more general and simpler to use, i.e., it involves only a sequential evaluation of expressions and the numerical resolution of a simple numerical integration. We derived the new formula using the method of vector potential, as opposed to Grover´s approach, which was based on the Neumann formula. We validated the new formula through a series of examples, which are presented here. Finally, we present the relationship between the two general formulas (i.e., Grover´s and our new one) explicitly (Example 12).