INDUCED MAGNETISATION 247 



be 47ncH. But <j is only imagined in order to account for the ex- 

 cess of intensity of field in the air over and above that which was 

 existing before the iron was introduced. We must, therefore, add 

 H, and the total intensity in the gap is 4?r/cH + H = /*H = B as 

 above. In calculating the energy in the iron, we have to deal with 

 the total induction, not the excess over that previously in the air 

 displaced. 



We observe that H is due to an external force applied to the 

 iron. In elastic stress and strain an external stress strains a body 

 until an internal stress is brought into play equilibrating the 

 external stress. Work is done against this internal stress in 

 increasing the strain, and energy is put into the body proportional 

 to internal stress and increase in strain. So in the magnetisation of 

 the iron, induction " magnetic strain " is produced by the ex- 

 ternal magnetising stress H until an equal internal stress is called 

 into play by the iron, and the energy put into the iron is the work 

 done against this internal stress, equal and opposite to H at each 

 step, as H increases from zero to its final value. 



Let the induction be increased by dB, by a small increase of 

 current in the solenoid. We may represent the process of increase 

 by imagining that North-seeking magnetism a^B/4?r is separated 

 from an equal quantity of South-seeking on the South side of the 

 gap and that it is carried round through the iron against the 

 intensity H exerted by the iron, this intensity being equal and 

 opposite to the external intensity due to the coil. 



If the length of the iron is / the work spent in the increase is 



and the total work spent in magnetising the iron will be 



H 



Since /UL is constant we may put dB = /mdH and we get total work 

 spent, or the energy supplied 



or, since la is the volume of the iron, the energy supplied per cubic 

 centimetre is 



B 2 



STT ' STT/X 



and if we assume that this energy is stored as magnetic energy in the 

 iron, these expressions give the energy per cubic centimetre. 



