Inductance between Two Loops in the Presence of Solid Conducting Bodies

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Abstract
The e.m.f. which is induced in a loop C2 by any given current flowing in a second loop G1 may be determined ill terms of the mutual inductance M of the two loops provided that the two loops are effectively alone in space. If however other conducting bodies are introduced into the neighbourhood of the loops, the eddy currents which are induced in these bodies disturb the electromagnetic field, thus changing the e.m.f. which is induced in C2 to a value which cannot be predicted in terms of M alone. Since it is the rule rather than the exception for inductance between two loops to take place in the presence of other conducting bodies, it is desirable to replace M by a more general quantity N (say) which will enable the required e.m.f. to be predictod in tho more general circumstances Using the well-established concept of transfer impedance as a guide, the form of N is discussed in general terms and, by moans of Maxwell's equations and standard boundary conditions, rigorous expressions for N ore obtained in each of the following cases : (i) Two circular co-axial loops and a co-axial sphere. (ii) Two circular co-axial loops and an infinite co-axial cylinder. (iii) Two rectangular loops and an infinito slab, the planes of the loops and the surfaces of the slab being parallel. There are two independent sub-cases (a) C1 and C2 on opposite sides of the slab (b) C1 and C2 on the same side of the slab The corresponding generalization of the self-inductance L of a loop is also deduced in cases (i), (ii) and (iii b) and an illustration in the use of the generalized characteristics is given in elementary circuit analysis.

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