and Electric Waves upon Small Obstacles. 



51 



magnetic field being /3=47rV,and the disk of radius R being 

 of infinite permeability, the potential at a distance great 



Fiar. 1. 



Fig-. 2. 



Fiff. 3. 



compared with E (but small compared with X) is by (27) 



yjr= — AnrV 



AWy 



3tt 



(132) 



By the symmetry the part of the plane x — external to the 

 disk is not crossed by the lines of flow, and thus it will make 

 no difference in the conditions if this area be filled up by a 

 screen of zero permeability. On the other hand, the part of 

 the plane x = represented by the disk is met normally by 

 the lines of flow. This state of things is indicated in fig. 2. 



The introduction of the lamina of zero permeability effects 

 the isolation of the positive and negative sides. We may 

 therefore now reverse the flow upon the negative side, giving 

 the state of things indicated in fig. 3. But the plate of 

 infinite permeability then loses its influence and may be 

 removed, so as to re-establish a communication between the 

 positive and negative sides through an aperture. The 

 passage from the present state of things to that of fig. 1 is 

 effected by superposition upon the whole field of /3=47rV, so 

 as to destroy the field at a distance from the aperture upon 

 the negative side and upon the positive side to double it. 



As regards the solution of the proposed problem we have 



then on the positive side 



4B 3 a 

 ^ = 87rV.y-47rV^-^ . . . (133) 



3ttv 3 



and on the negative side 



■ i v 4R3 



7 07T 



(134) 



E2 



