96 ADVANCED ELECTRICITY AND MAGNETISM. 



take the corresponding values of \i from the table in Art. 56. 

 Knowing the value of /* the length /, and the sectional area s 

 of each portion of the circuit, calculate the magnetic reluctance 

 <$ of each portion. Add these separate reluctances together 

 to get the total reluctance of the entire circuit, and multiply the 

 total flux $ by this total reluctance to get the required magneto- 

 motive force <$, according to equation (4). 



60. Work required to magnetize iron. When an iron rod is 

 magnetized by sending an electric current through a coil of wire 

 surrounding the rod, an opposing electromotive force is induced 

 in the coil by the growing magnetism of the rod, and the work 

 done in forcing the current against this opposing electromotive 

 force is the work expended in magnetizing the rod. 



The work W, in ergs, which is done in magnetizing V cubic 

 centimeters of iron from a given initial flux density <$' to a 

 given final flux density $", is given by the equation: 



W = 9C-d& (i) 



W* 



Proof. In order to avoid the complications which arise on 

 account of the perceptible demagnetizing action of the poles 

 of a short iron rod, let us consider a very long slim rod / centi- 

 meters in length and s square centimeters in sectional area. 

 Suppose this rod to be placed in a long coil having z turns of 

 wire per centimeter of length or Iz total turns. When the coil 

 of wire is first connected to the battery or other source of current, 

 the current in the coil (beginning at zero) rises in value during 

 the time that the rod is being magnetized, and during this time 

 the magnetic flux through the rod is growing in value. Let 

 d$/dt be the rate at which the flux is increasing at a given instant, 

 and let i be the value of the current at this instant. Then 

 Iz X d$/dt is the induced electromotive force in the coil which 

 at the given instant is opposing the current i, so that Iz X d$/dt 

 X i is the rate, dW/dt, at which work is being done at the given 

 instant in magnetizing the rod. That is: 



