CHAPTER X 

 STRESSES IN THE DIELECTRIC 



Tension along the lines of strain Pressure transverse to the lines of 

 strain Value of the pressure in a simple case This value will maintain 

 equilibrium in any case There may be other solutions of the problem 

 These stresses will not produce equilibrium if K is not uniform Quincke's 

 experiments General expression for the force on a surface due to the 

 electric tension and pressure The electric stress system is not an elasti< 

 stress system and is not accompanied by ordinary elastic strains. 



WE have shown that a charged conducting surface in air is pulled 

 out by a normal force 2-Tnr 2 per unit area, and that in a dirleetric of 

 specific inductive capacity K the pull become* ^Tro^/K per unit m 



Tension along the lines of strain. In accordance \\ith 

 the dielectric theory of electric action we must suppose that this 

 pull is exerted on the conductor by the insulating medium in 

 contact with it. Further, assuming that reaction is (<|ii.il and 

 opposite to action, the surface is pulling on the medium with an 

 equal and opposite force. 



Let AB, Fig. 89, be a small area a of a charged surface; 

 AC BD the tube of strain or force starting normally from it. 



The conductor is pulling on the medium in the tube with force 

 , since D = <r. Now consider the equilibrium 

 of a lamina of the medium between AB and 

 a parallel cross-section A'B very near to it. 

 The area of A'B' will also be a if A A is 

 small. The forces on the sides of this lamina 

 are negligible compared with those on tin- 

 ends, since the area of the sides i-> \anishingly 

 .small compared with the area of either end. 

 Then for equilibrium the part of the medium 

 above A'B' must pull on AA'B'B with a foivr 

 equal and opposite to that across AB, \i/. 



27rD 2 a/K. There is therefore a tension 



FIG. 89. 27rD 2 /K across A'B'. 



Now imagine the charged surface to be 



removed to A"B" some distance back, but so adjusted as to position 

 and charge that strain in the neighbourhood of A'B' remains the 

 same in direction and in magnitude. We can hardly suppose that 

 the stress across A'B' is altered, and so we obtain the result that a 



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