CHAP. X] ENERGY AND INDUCTANCE 185 



The inductance L is related in a simple manner to the electro- 

 motive force induced in the exciting electric circuit when the cur- 

 rent varies in it . Namely, the electric power supplied to the cir- 

 cuit or returned from the circuit to the source is equal to the rate 

 of change of the stored energy, so that we have from eq. (104) 



dW/dt=i(-e) =Li(di/dt), 

 or, canceling i y 



e = -L(di/dt), (107) 



The sign minus is used because e is understood to be the induced 

 e.m.f. and not that applied at the terminals of the circuit. There- 

 fore, when dW/dt is positive, that is, when the stored energy 

 increases with the time, e is induced in the direction opposite to that 

 of the flow of the current, and hence by convention is considered 

 negative. Inductance is sometimes defined by eq. (107), and then 

 eqs. (104) and (105) are deduced from it. The definition of L by 

 the expression for the electromagnetic energy seems to be a more 

 logical one for the purpose of this treatise, while the other defini- 

 tion in terms of the induced e.m.f. is proper from the point of 

 view of the electric circuit. 



Looking upon the stored magnetic energy as due to some kind 

 of a motion in the medium, eq. (104) suggests the familiar expres- 

 sions irav 2 and ^Kaj 2 for the kinetic energy of a mechanical system. 

 Taking the current to be analogous to the velocity of motion, the 

 inductance becomes analogous to mechanical mass and moment of 

 inert ia. The larger the electromagnetic inertia L the more energy 

 is stored with the same current. Equation (107) also has its 

 analogue in mechanics, namely in the familiar expressions mdv/dt 

 and Kdw/dt for the accelerating force and torque respectively. 

 The e.m.f. e represents the reaction of the circuit upon the source 

 of power when the latter tends to increase i the rate of flow of < !< - 

 tricity. While these analogies should not be carried too far, they 

 are helpful in forming a clearer picture of the electromagnetic 

 phenomena. 



The role of inductance, /., in t he current and voltage relations of 

 alternating-current circuits is treated in detail in the author's 

 !'.! clric Circuit. In this book inductance is considered from the 

 pnint of view of the magnetic circuit, i.e., asexpressed by eqs. (104) 

 to (lOro. In the next two chapters the values of inductance arc 



