ELECTROMAGNETS. MAGNETISM OF IRON. 



79 



(l) 



in which Z is the number of turns of wire in the coil, and i 

 is the strength of the current in the wire in abamperes. When 

 the current is expressed in amperes we have: 



10 



(2) 



Fig. 57. 



Proof of equation (i) above. Before proceeding to the deriva- 

 tion of equation (i), it is necessary to find an expression for the 

 total work W done in keeping the current i in a coil constant 

 while the magnetic flux through the opening of the coil is in- 

 creased by a specified amount <; W being expressed in ergs, 

 i in abamperes, and < in maxwells or lines. Now, while the 



d< 

 flux is increasing, a back electromotive force equal to Z 



ab volts is induced in the coil, and therefore (assuming the coil 

 to have zero resistance for the sake of simplicity of statement) 



d& 



an electromotive force e Z will have to act on the coil to 



at 



keep the back electromotive force from decreasing the current. 

 Consequently work will have to be done on the coil at the rate 



