

ELECTROMAGNETS. MAGNETISM OF IRON. 97 



dW d$ 



~df ~- lz/l ' Tt 

 so that: 



dW = lzi-d$ (2) 



in which dW is the amount of work done during the time that 

 the flux has increased by the amount d$ and while the current 

 has the mean value i. 



Now $ = cBs or d3> s-dcB from equation (i) of Art. 54, 

 and zi = M/^TT from equation (i) of Art. 17, so that the equation 

 (2), above, becomes: 



dW = 



47T 



or, since Is = V, we have: 



dW = 



47T 



or 



v 



In magnetizing a short iron rod, more work is done than is 

 accounted for by equation (i) above. The additional work 

 goes to establish the magnetic field in the neighborhood of the 

 magnetic poles of the rod. Equation (i), above, expresses the 

 work which is spent within the iron. 



61. Graphical representation of work done in magnetizing 

 iron. Let the curve opp', Fig. 67, be draw^i so that the co- 

 ordinates represent corresponding values of eB and 3t for a given 

 sample of iron. The branch op represents the values of cB 

 and c# when the iron is being magnetized for the first time, and 

 the branch pp' represents the values of $> and 3f when, after 

 the iron has been magnetized up to the point p, the value 

 of 3f is slowly reduced to zero. The curve of cB and &C for 

 decreasing values of 3t does not coincide with the curve for increasing 

 values of St. Now, as explained later, the total area opa repre- 

 sents the work done upon the iron in magnetizing it up to the point 

 p, and the area pp'a represents the work which is regained from 

 8 



