360 ELEMENTS OF ELECTRICAL ENGINEERING. 



6. Definition of flux-turns. Flux-turns due to a current in a 

 coil. The induced electromotive force in a coil of wire is equal 

 to Z x d<&jdt, where Z is the number of turns of wire in the 

 coil, and <I> is the flux through the coil (strictly, the flux 

 through a mean turn of the coil). But Z times the rate of 

 change of 4> is equal to the rate of change of the product Z. 

 Therefore Z<& is a quantity whose rate of change is equal to the 

 electromotive force induced in a coil. This quantity Z<& is 

 called the flux-turns. 



When a current flows through a coil the region surrounding 

 the coil and inside of the coil becomes a magnetic field, and the 

 lines of force of this magnetic field pass through the coil. That 

 is, the current in the coil produces magnetic flux through the 

 opening of the coil. Let <l> be the flux through the opening 

 of a coil due to a given current i in the coil, and let Z be the 

 number of turns of wire in the coil, and L the inductance of the 

 coil (everything being expressed in c.g.s. units). Then 



Z<J> = Li (5) 



This is evident when w r e consider that the self-induced electro- 

 motive force in a coil is equal to L x dijdt, according to Art. 4, 

 and that L x difdi is equal to the rate of change of Li ; but 

 the self-induced electromotive force is also equal to the rate of 

 change of Z<&, so that Z4> must be equal to Li* 



7. Calculation of inductance in terms of flux-turns per unit 

 current. f According to equation (5) the inductance of a coil is 

 equal to the quotient Z<&/i, where Z<E> is the flux-turns 

 through the coil due to current i in the coil. There are im- 

 portant cases in which the flux through the coil due to a given 

 current may be easily calculated so that the inductance of such a 

 coil may be easily determined. 



* In this argument algebraic signs are ignored and <I> is assumed to be equal to 

 zero when i is equal to zero. 



f Everything in this article is expressed in c.g.s. units except where expressly 

 stated to the contrary. 



