INTRODUCTORY. 5 



MAGNETIC FIELD DUE TO A CURRENT. 



6, When an electric current flows in a closed circuit consisting 

 of a single loop, a magnetic field is formed, and all the lines of 

 magnetic force either thread through the circuit or are within the 

 wire itself. Moreover, the number of lines interlinking with the 

 circuit is proportional to the current flowing in the circuit, provided 

 the permeability of the medium in which the circuit is placed is 

 constant. If the total number of lines passing through the circuit 

 is ^Vwhen a current of i C.G-.S. units is flowing in it, we then have 



N = Li. . (4) 



where L is a constant depending only on the geometrical form of 

 the circuit. 



L is called the Self-induction, or simply the Self- 

 inductance of the circuit, and is the total flux of magnetic 

 lines through the circuit when unit current flows round it. 



If, however, the closed circuit consists of a series of loops, so 

 that each line of magnetic force may encircle the circuit more than 

 once, the self-induction of the circuit is the sum of the products 

 of each line of force multiplied by the number of times it would 

 cut the circuit while being completely withdrawn when unit 

 current is flowing through the circuit. 



7. If there are two neighbouring closed circuits, one of which 

 carries unit current while no current flows round the other, the 

 number of lines of force interlinking the second circuit due to the 

 unit current in the first is called the Mutual Induction, or 

 Mutual Inductance, of the two circuits, and is denoted by 

 the letter M. It is, however, to be noticed again that if a line of 

 force due to the current in one circuit encircles the other circuit 

 n times, it must be reckoned n times over, since its effect is the 

 same as that of n lines of force encircling the circuit once. It may 

 be proved that l 



M = /7"'*-fr. (5) 



where ds and ds are elementary lengths of the two circuits, distant 

 r centimetres apart, and t is the angle between the tangents to the 



1 Maxwell's "Electricity and Magnetism," vol. ii. pp. 46 and 151, third 

 edition, 1802. 



