86 



ADVANCED ELECTRICITY AND MAGNETISM. 



the rod, flows through the rod, and passes out from the other end 

 of the rod, consists of two distinct parts which correspond to the 

 respective parts, a and b, of the field near the ends of the rod. 

 (a) The part a of the field is the original uniform field &C. 

 The lines of force of this field are shown by the parallel straight 

 lines in Fig. 63. The amount of magnetic flux which comes in 

 to one end of the rod and passes out from the other end of the 

 rod because of this uniform field cV, is <% lines. 



Fig. 63. 



(b) The part b of the field is the magnetic field due to the 

 pole m of the rod. The lines of force of this field are shown by 

 the radiating straight lines in Fig. 63. The amount of magnetic 

 flux which comes in to one end of the rod and passes out from 

 the other end of the rod, because of this field, is ^irm lines, as 

 explained in Art. 26. 



The total magnetic flux $ coming in to one end of the rod and 

 passing out from the other end is equal to the sum of the two 

 parts, a and b , so that we have : 



dtfs (i) 



and this flux passes through the rod. If &C is zero we have 



Now m = 3s from equation (i) of Art. 52, and therefore 

 equation (i) may be written: 



