ELEMENTARY ELECTRICITY AND MAGNETISM. II 



flux outwards across s. The tube is therefore called- a tube of 

 flux, or since the flux through it is everywhere unity it is often 

 called a unit tube. 



Similar unit tubes may be formed by lines of force passing out 

 from the peripheries of the other meshes of the net. In this way 

 the entire region of the magnetic field may be split up into unit 

 tubes and the magnetic flux across any surface anywhere in the 

 field will be equal to the number of these unit tubes which cross 

 the surface. 



These unit tubes may be represented each by a single line of 

 force drawn along its axis. Then the magnetic flux across any 

 surface anywhere in the field will be equal to the number of these 

 lines (unit tubes) which cross the surface. Lines of force are 

 always imagined to be drawn in a magnetic field so that each line 

 may represent a unit tube. 



7, Magnetfc flux from a magnet pole of strength m. Proposi- 

 tion. The number of lines of magnetic flux emanating from a 

 magnet pole of strength m is equal to ^rrm. That is : 



(5) 



in which <I> is the magnetic flux emanating from a magnet pole 

 of strength m. If the pole is a north pole, the flux ^rrm passes 

 out or diverges from it. If the p6le is a south pole, the flux /\.7rm 

 passes in or converges towards it. 



Proof of equation (5). Imagine a spherical surface of radius 

 r drawn with the pole m at its center. The area of this spherical 

 surface is 47JT 2 , the field intensity at every point on this spherical 

 surface * due to the pole m is mjr 2 according to equation (3), 

 and this field is everywhere at right angles to the spherical sur- 

 face. Therefore the magnetic flux across the spherical surface is 

 equal to M/(?*) x 47JT 2 which is equal to ^irm. 



Remark. The poles of a magnet are the places where mag- 

 netic flux passes from iron into air (north pole) or from air into 



* Except of course the small part of the surface where the bar of the magnet passes 

 through it. 



