ELECTROSTATICS 39 



the stress in the second layer is 



and the drop of potential across it is 



the stress in the inner layer is 



2q 

 1 = 



and the drop of potential across it is 



2 ff , _2 ?1 a 



The difference of potential between the conductor and the 

 sheath is 



E = EI -f- .2/2 4~ -^3 



2. # 2 2. R 3 . 2, #1 



(65) 



If j?^i, A^2 and A~ 3 are chosen inversely proportional to the inside 

 radii of the three layers, then the stress at these points will be 

 equal and will be the maximum stress in the field and 



9 - 2q - 2q 



^ ~ ~~ 



Curve 1, Fig. 34, shows the variation of potential gradient or 

 electrostatic stress from the conductor to the sheath. 



The stress in the dielectric is much more uniform than in the 

 case of the same cable insulated with a single dielectric. 



The thicknesses of the three layers have been assumed to be 

 equal. 



From these examples it is seen that a field in which the stresses 

 are not uniform can be made more uniform by grading the in- 

 sulation, that is, using a material of high dielectric constant in 

 the part of the field where the stress tends to be a maximum and 

 gradually decreasing the dielectric constant in the parts where 

 the stress tends to be low. 



From equation 65 the charge per centimeter length of the con- 



