ELEMENTARY ELECTRICITY AND MAGNETISM. 



be done if the induced current did not exist. This additional 

 work is the work which is expended in producing the induced 

 current. 



A more general aspect of Lenz's law is given in Art. 26 where 

 the relation between the electric generator and the electric motor 

 is discussed. 



23, Electromotive force induced in a straight wire moving side- 

 wise across a uniform magnetic field. With the help of Lenz's 

 law the fundamental law of induced electromotive force may be 

 derived. For this purpose 

 it is sufficient to consider 

 the simplest case, namely, 

 the motion of a straight 

 wire sidewise across a uni- 

 form magnetic field. 



A straight wire AB., 

 Fig. 15, slides sidewise at 

 a velocity of v centimeters Figt 15> 



per second along two straight wires or rails CA and DB distant 

 / centimeters from each other. The rails are connected at CD 

 so that ABCD is a closed circuit. The whole arrangement is 

 placed in a uniform magnetic field of intensity 3{, the direction 

 of the field being perpendicular to the plane ABCD and towards 

 the reader. 



The motion of the wire AB induces in it an electromotive 

 force ; this electromotive force produces a current in the circuit 

 ABCD, and because of this current the wire AB is pushed side- 

 wise by the magnetic field with the force F, of which the value 

 in dynes is given by the equation 



F= Ildf (6) 



in which 7 is the strength of the induced current in abamperes. 



Now Fv is the rate in ergs per second at which work is done in 



moving the wire AB against the opposing force F t and, from 



Lenz's law, this must be equal to the rate El at which work is 



