CHAP. XIII] TORQUE AND TRACTIVE EFFORT 257 



I of the conductor. Substituting the value of e from eq. (27), 

 Art. 24, we have 



Fds/dt=iBlv, 

 or, since ds/dt=v, 



F=iBl (193) 



In this expression i is in amperes, B is in webers per sq.cm., 

 I is in cm., and F is in joulecens. With other units the formula 

 contains a numerical factor. 



Formula (193) may be used also with anon-uniform field, and 

 also when the direction of the conductor is not at right angles 

 to that of tin* line of force. In such cases the formula becomes 

 dF=iBdl, where dF is the force acting upon an infinitesimal 

 length dl of the conductor, and B is understood to be the com- 

 ponent of the actual flux density perpendicular to dl. 



As an application of formula (193), consider the attraction 

 or the repulsion between two straight parallel conductors carrying 

 currents t'i and 1*2, and placed at a distance 6 from each other. 

 The circuit of each conductor may be considered dosed through 

 a concentric cylindrical shell of infinite radius, as in Art. 60. 

 It is apparent from symmetry that the field produced by each 

 system gives no resultant force with the current in the same 

 system. Thus, the mechanical force is due to the action of the 

 field 1 upon the current 2, and vice versa. 



The flux density due to the system 2 at a distance 6 from 

 the conductor 2 is =/.i2/2;r&, so that, according to eq. (193), 



F=friiiyl/ 2^6 joulecens, (194) 



where /*= 1.257X 10~ 8 . In kilograms the same formula is 



F-2.04t 1 t 2 tf/6)10- 8 , (194a) 



provided that / and 6 are measured in the saino units. The 

 force is an attraction or a repulsion according to whether tin- 

 two currents are flowing in the same or in the opposite directions. 

 When ii-i2, this formula checks with that given in prob. 19 

 i bove, 



Formula (193) applies also to the tangential force betv 

 the field and armature conductor in any ordinary generator or 

 motor, provided that (o) the conductors are placed upon a 

 smooth-body armature, and (6) the conductors arc distributed 



