114 COEFFICIENTS OF INDUCTION. 



CHAPTER V. 

 COEFFICIENTS OF INDUCTION. 



755. INDUCTION IN A CIRCUIT. We may still assume as a 

 first approximation (722) that the current which traverses a wire is 

 concentrated on the axis of the conductor. 



The induction of a field in a circuit is then the flow of force 

 across a surface S, bounded by the axis of the wire which constitutes 

 the circuit, and the relative error made by this mode of calculation is 

 very small as long as the dimensions of the surface are very great 

 in comparison with the diameter of the wire. If the medium is 

 magnetic, in order to have the flow of induction, we must multiply 

 the force by the coefficient of induction or of magnetic permeability 

 /K O (393) of the medium. Denoting by F 7l the mean component of 

 the force perpendicular to the surface S, the induction of the field in 

 the circuit is /^ F n S. 



If the field is produced by a current which traverses a second 

 circuit, the flow of force is proportional to the intensity I of this 

 current, and may be represented by MI ; the flow of induction is 

 then />i ML The factor M is the coefficient of mutual induction (519) 

 of the two circuits ; it is that portion of the flow of force starting 

 from one of the circuits for unit current which traverses the surface 

 bounded by the second. 



In like manner the coefficient of self-induction of a circuit is the 

 flow of induction which it emits for unit current, and which traverses 

 the surface bounded by the axis of the wire. 



These simple considerations suffice in most cases, but if the 

 section of the conducting wires cannot be neglected, it is necessary 

 to have recourse to the general properties of the electromagnetic 

 field. 



756. PARALLEL CURRENTS. Let us consider, in the first case, 

 a system of parallel rectilinear currents, so long that, in a plane 

 perpendicular to the currents, the distribution of forces is inde- 

 pendent of the manner in which the ends of the conductor are 

 connected with each other and with the sources of electricity. 



