4 8 



ADVANCED ELECTRICITY AND MAGNETISM. 



"flux through the opening of the coil" has a somewhat compli- 

 cated meaning. It is a fundamental principle in geometry that 

 in considering the area of a multiple loop each part of the area 

 must be counted n times, where n is the number of loops 

 encircling that part. Thus the shaded area A in Fig. 40 would 



Fig. 40. 



Fig. 41. 



be counted twice, and the area B would be counted once. 

 Similarly in considering the magnetic flux through the opening 

 of a coil each part of the flux is counted n times where n is 

 the number of turns of wire encircling that part. Thus the flux 

 A in Fig. 41 would be counted twice and the flux B would be 

 counted once. If the flux A is one million lines (maxwells) and 

 if B is half a million lines, then the flux <1> through the opening 

 of the coil would be thought of as (2 A + B) or 2,500,000 lines. 

 With this explanation of the meaning of 3>, equation (i) becomes 

 entirely general, and the definition of inductance as above given 

 becomes entirely general. 



Another point of view. Mean flux per turn. In many cases 

 it is convenient to consider the average or mean flux per turn of 

 wire in a coil, and to multiply this by the number of turns to get 

 the quantity $ as above defined. Let & be the average or 

 mean flux per turn, then the quantity <J>, as above defined, is 

 equal to Z<' where Z is the number of turns of wire in the 

 coil. Therefore equation (i) may be written: 



Z& = LI (2) 



