CHAP, x.] ELECTRICITY AND MAGNETISM. 369 



circuits when each carried unit current. Now, if two 

 such circuits approach one another so as actually to 

 coincide, the mutual induction becomes a self-induc- 

 tion of the circuit on itself. For every circuit there is a 

 coefficient of self-induction^ whose value depends upon the 

 form of the circuit, and which will be greater if the 

 circuit be coiled up into many turns, so that one loop of 

 the circuit can induce lines-of-force through another loop 

 of the same. Let L represent the coefficient of self-in- 

 duction of one circuit, and L' that of a second circuit 

 equal to the first. When these two circuits coincide with 

 one another their coefficient of mutual induction (i.e., the 

 number of lines-of-force running through both circuits, 

 each carrying unit current) M will be equal to L + L'; 

 or, L = J M. Now for two coincident circuits having 

 n turns each, and each of area S (by Art. 397), 



M = 4?rS^ 2 ; 



hence the coefficient of self-induction for one circuit 

 of n turns coiled up in one plane, 



L = 27TS/Z 2 . 



The existence of self-induction in a circuit is attested by 

 the so-called extra-current, which makes its appear- 

 ance as a bright spark at the moment of breaking circuit. 

 If the circuit be a simple one, and consist of a straight 

 wire and a parallel return wire, there will be little or no 

 self-induction; but if the circuit be coiled up, especially if 

 it be coiled round an iron bar, as in an electromagnet, 

 then on breaking circuit there will be a brilliant spark, and 

 a person holding the two ends of the wires between which 

 the circuit is broken may receive a slight shock, owing 

 to the high electromotive-force of this self-induced extra 

 current. The extra - current due to self-induction on 

 "making" circuit is an inverse current, and gives no spark, 

 but it prevents the battery current from rising at once to 

 its full value. The extra-current on breaking circuit is 

 a direct current, and therefore increases the strength of 

 the current just at the moment when it ceases altogether. 



2B 



