276 MAGNETISM 



The relations between permeability and magnetising force 

 vary greatly with the quality of the iron or steel tested. The 

 softer the iron the greater the maximum permeability. With 

 steel the permeability is in general lower the harder tin- steel. 

 Alloys of iron with manganese, tk manganese steel," have been 

 made with a permeability less than 1'5, and Hopkinson found 

 that a certain specimen of nickel steel containing .."> per cent, of 

 nickel had practically a constant permeability of 1*5. 



Nickel and cobalt. The methods which we have described 

 for iron may be used also for nickel and cobalt, and similar results 

 are obtained, though the magnetisation and permeability for a 

 given magnetising force are much less than for iron. For an 

 annealed nickel wire Ewing found that K attained a maximum 

 value of 23'5 when the field was 9'5. This corresponds top = 2i)(>. 

 In general the saturation value of I for nickel is a third or a fourth 

 the value for wrought iron. Cobalt has less susceptibility than 

 nickel in weak fields, but greater in strong fields. 



The hysteresis loop and the energy dissipated in 

 a cycle. We have seen that if we start with demagnetised 

 iron and apply a magnetising force gradually increasing to a 

 maximum of considerable value + H m , and if then we carry H 

 through a complete cycle + II m , O, H m , O,-f H m , the magnetisa- 

 tion I and the induction 13 return to very nearly the same val 

 and the magnetisation curve forms a very nearly closed loop. 

 Probably I and B do not return to exactly the same values. 

 But successive repetitions of the cycle give nines \u\ nearly 

 overlying the first, and the longer the cycle is repeated the more 

 nearly do the sucoettive curves coincide. \\Y shall suppose that 

 the stage is reached in which \\c may take the magnetisation 

 curve as a closed loop the hv>tcresi, loop. 



In each cycle a certain amount of energy is dissipated and 

 appears as heat in the iron. We may calculate the energy dis- 

 sipated in a way somewhat different from that already given in 

 Chapter XIX. We shall suppose that we are using the ring 

 method and that the magnetising coil is wound so closely on the 

 iron that the induction may be considered as all within the iron. 



Let E be the E.M.F. put on to the magnetising coil from 

 outside. Let B be the number of induction tubes through unit 

 area of the iron, and let a be the area of its cross-section. Then 

 aB is the total induction. If there are n turns of the coil the 

 virtual number of tubes through it is ;iaB. If C is the current 

 through the coil and R its resistance the current equation is 



or 

 Multiplying by C, 



CEdt = naCdB 



