44 ADVANCED ELECTRICITY AND MAGNETISM. 



this induced electromotive force in abvolts is equal to the rate 

 of change of $ in lines of force (maxwells) per second. That is: 



Experiment shows that this equation is true not only when the 

 change of magnetic flux is due to motion as in Fig. 31, but also 

 when the change of magnetic flux is due to a varying magnetic field 

 or to a varying state of magnetism of an iron core as in the trans- 

 former or induction coil. 



The negative sign is chosen in equation (4) for the following 

 reason: The flux $ is thought of as going through the opening of 

 a circuit in the direction of the magnetic field. Suppose that $ 



d3> 



is increasing. Then is positive, and the induced electromotive 

 dt 



force E is in the direction around the circuit in which a left- 

 handed screw would have to be turned in order that it might travel 

 in the direction of <. If we choose the direction-through-the- 

 opening-of-a-circuit which is to be considered as positive, then 

 the positive direction around the circuit is considered to be the 

 direction in which a right-handed screw would have to be turned 

 in order that the screw might travel in the positive direction 



d$ 

 through the opening of the circuit. Therefore when is 



positive E is negative. 



Equation (4) expresses the electromotive force which is induced 

 in a single turn of wire. When a region of changing magnetic 

 flux is encircled by Z turns of wire, then the induced electro- 

 motive force is multiplied Z times, and equation (4) becomes: 



>--** 



d$ 

 in which represents the rate of change of the flux in lines of 



force (maxwells) per second, and E is the induced electromotive 

 force in abvolts. 



