122 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



Fv = El (i) 



and from equation (28), in Art. 52, 



F=IIH 

 whence, substituting this value of F in equation (i), we have 



E=lHv (42) 



that is, the electromotive force induced in a wire / centimeters 

 long, moving sidewise at a velocity of v centimeters per second 

 across a uniform magnetic field of intensity H is equal to the 

 product IHv. This product expresses the induced electromotive 

 force in c.g.s. units or abvolts, one abvolt being an electromotive 

 force which will do work at the rate of one erg per second 

 in maintaining a current of one abampere. One volt equals 

 io 8 abvolts. 



65. Expression of induced electromotive force in terms of lines 

 of force cut per second. During t seconds the sliding piece 

 BB' ', Fig. 82, moves over a distance vt and sweeps over Ivt 

 square centimeters of area. The product of this area by the field 

 intensity H gives the number of lines of force <I> which pass 

 through the area according to equation (18), and this is the 

 number of lines of force cut by the moving wire in / seconds, 

 that is, 



4> = IHvt (i) 



Dividing both members of this equation by /, we have 



4> 



- = lHv 



v 



but &/t is the rate at which the moving wire BB' cuts lines 

 of force, or, in other words, it is the number of lines of force cut 

 per second, and IHv is the electromotive force in abvolts induced 

 in the wire, according to equation (42). Therefore the electro- 

 motive force in abvolts induced in a moving wire is equal to the 

 number of lines of force cut per second by the moving wire. This 

 result is true for any wire, straight or curved, moving in any 



