88 ELECTRICAL ENGINEERING 



The henry is defined as the inductance of a circuit in which a 

 counter e.m.f. of one volt is generated when the current is chang- 

 ing at the rate of one ampere per second. 



The relation between the two units of inductance is found as 

 follows ; 



/ di 

 e = -r c.g.s. units 



di 

 = X -j- 10~ 8 volts, X and i in c.g.s. units, 



di 

 >-T 10~ 9 volts, X in c.g.s. units, i in amperes, 



r di ,, 



= -L 5 volte, 



and, therefore, 



1 henry = 10~ 9 c.g.s. units of inductance. . . (125) 



65. Inductance of Circuits Containing Iron. If a solenoid 

 with n turns is wound on an iron ring of section A sq. cm. and 

 mean length I cm., the flux produced by a current i c.g.s. units is 



.. 

 lines, 



where // is the permeability of the iron; the flux per unit current is 



4:TrnAfJL.. 



0i = -T = -- j lines, 

 ii i 



and the inductance is 



X = TKfri = - -j - c.g.s. units. 



It is proportional to the square of the number of turns as seen in 

 the last example, but it also depends on the permeability of the 

 iron and is therefore not a constant quantity. When the cur- 

 rent in the solenoid is small, the iron is unsaturated, the per- 

 meability is high, the flux per unit current is large and therefore 

 the inductance is large. When the current is large, the iron is 

 saturated, the permeability is low, the flux per unit current is 

 small and therefore the inductance is small. 



The inductance of circuits containing iron or other magnetic 

 materials is not constant, but decreases as the density of the 

 induction increases, since the permeability decreases. (See Art. 49.) 



