ELF Coaxial Partial Mutual Inductance Part I - Theory

This paper presents a novel expression for the partial mutual inductance between the core and screen of a coaxial or pipe-type cable. This partial mutual inductance describes the electromotive force in the screen when there is current in the core and not the screen. This differs from the conventional expression for the inductance of a coaxial cable whose derivation supposes balanced opposing currents flowing in the core and screen. The magnetic field generated by a time-varying current in the core with no balancing current in the screen is an expanding field of infinite extent. This contrasts with the loop inductance of a coaxial cable, which exists only within the cable confines. The expanding nature of the field through a surface limits the forms of Faraday's Law that can be applied to describe the inductance being defined. The partial mutual inductance is determined by applying Maxwell-Faraday's Law to a surface with two closed but independent boundaries. The result aligns with field tests conducted on coaxial power cables, which indicate that the electromotive force generated by the current within the coaxial screen depends solely on the cable length and the frequency of excitation. Part II of this paper presents experimental support for this theory.