38 ADVANCED ELECTRICITY AND MAGNETISM. 



exerted on the wire by the field is equal to IIH dynes where 

 / is the length of the wire in centimeters and / is the strength of 

 the current in the wire in abamperes. 



Fig. 31. 



Dots represent magnetic lines of force which are perpendicular to the plane of 

 the paper. 



Suppose the wire to be moving in the direction of the dotted 

 arrow at a velocity of v centimeters per second. Then work 

 will be done at the rate of Fv ergs per second in moving the wire 

 in opposition to the force F; but, according to Lenz's principle, 

 all of the work thus spent reappears as the electrical work done 

 by the induced electromotive force in maintaining the current /. 

 Let E be the electromotive force in abvolts which is induced in 

 the moving wire, then El is the rate at which work is done by 

 the induced electromotive force in maintaining the current. 

 Therefore, according to Lenz's principle we must have 



whence we get 



El = Fv = HHv 

 E (in abvolts) = IHv 



(i) 



that is, the electromotive force E in abvolts which is induced in 

 the moving wire in Fig. 31 is equal to the product of the length 

 / of the wire in centimeters, the intensity, H, of the magnetic 

 field in gausses, and the velocity, v, of the wire in centimeters 

 per second. 



