LEGA L NOT ICE lo(Governmen t sponsored work. Neither the UnJted This repart was prepared as an accoun Ung n behalf of the CommJeeto n: States, nor tbe Commissio n, nor any person ac o ed o implied with respect to the accu-A. Makes any warranty or re~r:~~: ::~=~::s con~ed tn th.ts rePort, or that the use racy, completene ss, or useful nee, dJ 1 ed tn this report may not tnCrtnge of any tnformaUon , apparatus, method, or process sc oe privately owned rights; or t to th use of or for damages resulting from the B. Assumes any UablUUes with r=c or prO:ess di~closed in thJs report. use of any tnformaUon , apparatus, me ' behalf f the CommtSsio n" includes any em-As used in the above, "perso:ea~: :u~::m('lln yP.: of lll\lCh contractor , to the extent that ployee or contractor of the Cu@mi 1 • t t or employee of eucb contractor prepares, sucb ewiJ\uyee or contract"'" nf the Comm ee on, uant to biB empluywcl1 t or oontrlM:t dtesem.lne. tee, or provides e.ccees to, any tnformatto~ pure wt th the Comm!eeto n, or bis employmen t with such contractor .

LEGA L NOT ICE lo(Governmen t sponsored work. Neither the UnJted This repart was prepared as an accoun Ung n behalf of the CommJeeto n: States, nor tbe Commissio n, nor any person ac o ed o implied with respect to the accu-A. Makes any warranty or re~r:~~: ::~=~::s con~ed tn th.ts rePort, or that the use racy, completene ss, or useful nee, dJ 1 ed tn this report may not tnCrtnge of any tnformaUon , apparatus, method, or process sc oe privately owned rights; or t to th use of or for damages resulting from the B. Assumes any UablUUes with r=c or prO:ess di~closed in thJs report. use of any tnformaUon , apparatus, me ' behalf f the CommtSsio n" includes any em-As used in the above, "perso:ea~: :u~::m('lln yP.: of lll\lCh contractor , to the extent that ployee or contractor of the Cu@mi 1 • t t or employee of eucb contractor prepares, sucb ewiJ\uyee or contract"'" nf the Comm ee on, uant to biB empluywcl1 t or oontrlM:t dtesem.lne. tee, or provides e.ccees to, any tnformatto~ pure wt th the Comm!eeto n, or bis employmen t with such contractor .

The vector potential has been obtained for a coil coaxial with an arbitrary number of cylindrical conductors. The derivation is quite general and employs an iterative process that has been adapted to computer programs. After the vector potential has been obtained, it is used to calculate the mutual and self-impedance of multiple and single coils, the effect of defects in the conductors on the mutual and self-impedances, and the induction heating density in the conductors.

No abstract

The general theory for the vector potential produced by a sinusoidal current of finite cross section has been developed in a preceding paper.1 In the present work, this theory is applied to a coil between a number of plates of finite electrical conductivities and permeabilities. Linear, isotropic, and homogeneous media are assumed throughout. The Green's function solution is first obtained, and the principle of superposition is then used to effect the desired result. A number of physically observable phenomena, such as the impedance, the power loss due to the presence of the conductors, and the time-averaged electromagnetic force on the conductors are subsequently calculated from the vector potential. The treatment is sufficiently general to allow the solution of a number of difficult electromagnetic induction problems, while each of the expressions obtained for the physically observable phenomena is in terms of an infinite integral that may readily be evaluated on a computer. In all cases for which experimental measurements have been made, the agreement between calculated and observed values is within the limits of experimental error. Preliminary investigations of other cases tend to support the validity of the corresponding theoretical expressions.