CHAP. XIIIJ TORQUE AND TRACTIVE EFFORT 253 



increase the energy stored in the magnetic circuit. The increase 

 in the stored energy is 



and the energy supplied from the line is calculated as follows: 

 The average voltage induced during the motion of the plunger 

 is 0^=1^2 -Li)/t, where t is the duration of the motion. The 

 energy supplied from the line is therefore 



Thus, the energy supplied from the line is twice as large as the 

 work performed, and we have the following important law 

 (due to Lord Kelvin) : When in a singly excited magnetic circuit, 

 without saturation, a deformation takes place, at a constant cu 

 the energy supplied from the line is divided into two equal parts, 

 one half increasing the stored energy of the circuit, the other half 

 being converted into mechanical work. 



. According to this law we have, for a constant current electro- 

 magnet, that the mechanical work done is equal to the increase 

 in the energy stored in the magnetic field. Hence 



Thus, 



*di ..... (186) 



or, if the partial linkages are negligible, 



(2-Si); . . . (187) 

 -i) ..... (188) 



When a magnet performs a rotary motion (Fig. 63), the 

 preceding formulae are modified by substituting TdO in place of 

 Fds, or T ave (0 2 Ofi in place of F aw ( 2 -i). Here T is the torque 

 in joules and (02 Oi) or dO is the angular displacement of the 

 armature in radians. Or else, in the foregoing formulae F may 

 be understood to stand for the tangential force, and the dis- 

 placement to be cte-r dO, where r is the radius upon which 

 the force F is acting. Thru t ho torque is T- Fr. If, for instance, 

 we apply eq. (179) to a rotary motion, it becomes 



(189) 

 The other equations may be written by analogy with this one. 



