40 ADVANCED ELECTRICITY AND MAGNETISM. 



field will be equal to the number of these lines of force which cross 

 AA. 



26. Proposition. The amount of magnetic flux <f> which 

 emanates from a north magnet pole is equal to 471- If, where M 

 is the strength of the pole. Imagine a spherical surface of radius r 

 drawn with its center at the pole M as shown in Fig. 34. The 



Fig. 34. 



area of this spherical surface is ^irr 2 (neglecting the small portion 

 of the sphere which falls inside of the slim magnet at b). The 

 magnetic field at the spherical surface due to M is everywhere at 

 right angles to the surface, and its intensity at the surface is 



M 



according to Art. 9. Therefore, the magnetic flux 



II 



M 



across the spherical surface is equal to 4?rr 2 X -7 or \^M, 



according to Art. 25. But the flux across the spherical surface 

 is the flux that emanates from the pole. Therefore the flux that 

 emanates from the pole is ^irM. 



Magnetic flux through the steel bar at b, Fig. 34. The 

 magnetic flux which emanates from the north pole M in Fig. 34, 

 enters the magnet at its south pole and passes along the bar to 



