ON FARADAY'S LINES OF FORCE. 



IX. Effect of the core of the electro-magnet. 



Now let us suppose a sphere of diamagnetic or paramagnetic matter intro- 

 duced into the electro-magnetic coil. The result may be obtained as in the 

 last case, and the potentials become 



n 3k r 



The external effect is greater or less than before, according as k' is greater 

 or less than k, that is, according as the interior of the sphere is magnetic or 

 diamagnetic with respect to the external medium, and the internal effect is 

 altered in the opposite direction, being greatest for a diamagnetic medium. 



This investigation explains the effect of introducing an iron core into an 

 electro-magnet. If the value of k for the core were to vanish altogether, the 

 effect of the electro-magnet would be three times that which it has without 

 the core. As k has always a finite value, the effect of the core is less than this. 



In the interior of the electro-magnet we have a uniform field of magnetic 

 force, the intensity of which may be increased by surrounding the coil with a 

 shell of iron. If k' = 0, and the shell infinitely thick, the effect on internal points 

 would be tripled. 



The effect of the core is greater in the case of a cylindric magnet, and 

 greatest of all when the core is a ring of soft iron. 



X. Electro-tonic Junctions in spherical electro-magnet. 



Let us now find the electro-tonic functions due to this electro-magnet. 

 They will be of the form 



=o, A>=<uz, %= -<*y> 



where o> is some function of r. Where there are no electric currents, we must 

 have a,, 6,, c t each = 0, and this implies 



d 

 Tr 



the solution of which is 



