CHAPTER XIII 



THE MECHANICAL FORCE AND TORQUE DUE TO 

 ELECTROMAGNETIC ENERGY. 



69. The Density of Energy in a Magnetic Field. The reader 

 is already familiar with the fact that a certain amount of energy 

 is required to establish the flux within a magnetic circuit, and 

 that this energy remains stored in the field. This stored energy 

 may be conveniently thought of as the kinetic energy of vor- 

 tices around the lines of force (Art. 3). Various expressions 

 for the total stored electro-magnetic energy are given in Arts. 

 57 and 58; the problem here is to find a relation between the 

 distribution of the flux density and that of the energy in the 

 field. 



Consider . first the simplest magnetic circuit (Fig. 1) con- 

 sisting of a non-magnetic material. According to the last eq. 

 (99), the total energy stored in such a circuit is 



joules, ..... (162) 



if is in webers, I and A in cm., and /*= 1.257X10" 8 henrys 

 per cm. cube. The volume of the field is V=IA cubic cm. 

 Since the flux density is uniform, the energy is also uniformly 

 distributed, and the density of the energy is 



Denoting the density of the energy W/V by W, and introducing 

 the flux density B=d>/A, we get 



W' = iB 2 /// joules per cu.cm. . . . (163) 



Either B or // can be eliminated from this expression by means 

 of the relation B=fiH, so that we have two other expressions 

 for the density of the energy: 



....... (164) 



(165) 



240 



