53$ PARTICULAR CASES OF INDUCTION. 



As the external electromotive force is constant, this work is a 

 maximum when the motion reduces the strength of the current 

 by one-half, and the efficiency is then equal to 0.50. 



If the external work is very small, the velocity of the motor 

 increases very rapidly with or without limit according to the mode 

 of construction; the electromotive force of induction tends to 

 become equal to the external electromotive force, and the efficiency 

 tends towards unity. 



557. ELECTROMOTORS. When an electrical motor is set in 

 motion by an extraneous machine, it becomes the seat of an 

 electromotive force, opposite in sign to that which would produce 

 the motion, and the circuit which constitutes it is, in general, 

 traversed by an electrical current. The apparatus is then a 

 producer of electricity, or an electromotor. 



Suppose that owing to any temporary cause there is in the 

 circuit a current of the strength / ; if the work E/, absorbed by 

 the electromotive force of induction, is greater than the thermal 

 energy disengaged in the conductors, the current will go on 

 increasing until 



(63) E I = PR. 



If the condition E>/R holds for an infinitely small current, 

 the machine once in motion will prime itself, and for a steady con- 

 dition will produce a current denned by the preceding equation 

 (61). When, on the contrary, E</R for an infinitely small current, 

 the external work cannot create and maintain an electrical current, 

 unless there is artificially introduced into the circuit a current of 

 such strength that the condition E>/R is realised, after which 

 the extraneous electromotive force could be suppressed without 

 the current ceasing. 



A machine used as an electromotor is therefore capable, or not, 

 of creating an electric current, or of keeping up a current already 

 established, according to the value of the total resistance, or, what 

 produces an analogous effect, according to the kind of external 

 work which the current is to produce. Since the electromotive 

 force of induction, other things being equal, is proportional to the 

 velocity of the machine, we see that for a given total resistance, 

 and given external work, the electromotor will be able to produce 

 and maintain a current the more rapidly, the greater is its velocity. 



Let us consider two extreme cases : 



ist If a machine consists of permanent magnets which produce 

 an invariable field in which the conducting wires move (take 



