10 



ELEMENTS OF ELECTRICAL ENGINEERING. 



are closed or reentrant lines.* A closed surface, such as a 

 sphere, may be imagined to be drawn in a moving liquid, and a 

 certain amount of liquid may flow into the enclosed region across 

 a portion of the bounding surface, if so, then an exactly equal 

 amount of liquid must flow out of the enclosed region across 

 some other portion of the bounding surface. Similarly, if mag- 

 netic flux enters an enclosed region through one portion of the 

 bounding surface, an exactly equal flux must pass out of 

 the enclosed region across some other portion of the bounding 

 surface, or in other words, the total magnetic flux across a closed 

 surface is zero. 



A clear idea of the manner in which magnetic flux is distributed 

 in space may be obtained as follows : Imagine a net stretched 

 across any given magnetic field and imagine the meshes of the 

 net to be large in area where the field is weak or where the field 

 is inclined to the netted surface so that the product s&Ccos 6 is 

 unity for each mesh of the net. 



Imagine lines of force to be drawn through the magnetic field 

 starting from every point in the periphery of one of the meshes 

 of the net. These lines of force form a tube-like surface having 



the given mesh for a base. 

 The magnetic flux across the 

 base of this tube, b, Fig. 3, is 

 unity by supposition. The 

 magnetic flux through any 

 given surface s stretched across 

 the tube any where is also unity 

 For the given surface s, the 

 base b y and the walls ww of 

 the intervening portion of the 



tube constitute a closed surface across which the total flux in- 

 wards is zero ; but the flux across the walls ww is every- 

 where zero since these walls are everywhere parallel to the lines 

 of force ; therefore the flux inwards across b is equal to the 



* Unless the field extends to infinity. 



