146 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



in which L is the mass of the body and dijdt is the rate at 

 which its velocity changes. Equation (49) is therefore analogous 

 to the fundamental equation in mechanics which expresses the 

 relationship between unbalanced force, mass and acceleration. 



Starting from the fact that force equals mass times accelera- 

 tion, it can be shown that the kinetic energy of a moving body is 

 equal to one-half its mass times its velocity squared, suitable 

 units being employed. The same argument reversed would show 

 that force must be equal to mass times acceleration if kinetic 

 energy is equal to one-half mass times velocity squared ; and an 

 exactly similar argument would establish equation (^ <?) on the basis 

 of equation (48]. 



Self-induced electromotive force. When one pushes on a body 

 causing its velocity to increase the body reacts and pushes back 

 on the hand. This reacting force is equal and opposite to the 

 acting force which is causing the increase of velocity. When the 

 velocity of the body is increasing, its reaction is a force opposed 

 to its motion, and, when the velocity of the body is decreasing, 

 its reaction is a force in the direction of its motion. 



Similarly when an electromotive force acts upon a circuit and 

 causes the current to increase or decrease, the changing current 

 reacts, and the reacting electromotive force is equal and opposite 

 to the acting electromotive force which is causing the current to 

 change. Therefore from equation (49) we have 



di 

 *=- L dt (5) 



in which e is the reaction of the changing current in a circuit of 

 which L is the inductance, and di/dt is the rate at which the 

 current is changing. This reaction of a changing current is 

 called self-induced electromotive force. 



78. Growth of current in an inductive circuit. A steady force 

 E begins to act upon a boat at a given instant, starting it from 

 rest. At the given instant the velocity of the boat is zero, the 

 frictional drag of the water is zero, and all of the force is used to 



