INDUCED ELECTROMOTIVE FORCE. 123 



manner in any magnetic field, uniform or non-uniform, although 

 the derivation here given applies to the motion of a straight wire 

 across a uniform field. 



66. Expression of induced electromotive force in terms of rate of 

 change of magnetic flux through a circuit.* The total magnetic 

 flux through the circuit ABB'A', Fig. 82, is given by equation 

 (i), Art. 65, and the rate at which the moving wire BB' cuts 

 lines of force is the rate of increase of <E>. Therefore the electro- 

 motive force induced in a circuit is equal to the rate of change of 

 the magnetic flux through the circuit, that is, 



Experiment shows this equation to be true when the change of 

 magnetic flux is due to motion and also when the change of mag- 

 netic flux is due to varying strength of the magnetic field. 



The negative sign in equation (43) has no immediate importance. 

 It is chosen in accordance with the following convention. A 

 right handed screw with its axis parallel to the magnetic field H 

 (directed towards the reader in Fig. 82) would have to be turned 

 in a direction opposite to the flow of induced current produced by 

 an increasing flux in order to make the screw travel in the direc- 

 tion of H. It is therefore convenient to look upon the induced 

 current or the induced electromotive force as negative when 

 d<&jdt is positive. 



Equation (43) expresses the electromotive force induced in a 

 single turn of wire. When a region of changing magnetic flux is 

 surrounded by Z turns of wire, then equation (43) expresses the 

 electromotive force induced in each turn of wire, and the total 

 electromotive force is 



E=-Z~ t (44) 



* Let it be remembered that the fundamental action upon which induced electro- 

 motive force depends is the cutting the lines of force by a moving conductor or the 

 sweeping of moving lines of force past a stationary conductor. 



