ELECTROSTATICS 37 



If the conductor is raised to a potential E and the sheath is 

 grounded, the potential at any point P distant r cm. from the 

 centre of the conductor may be found as follows: 



Assume that the charge per centimeter length of the conductor 

 is q units, then the flux density at P is 



= lines per square centimeter, 

 and the electrostatic force or stress in the medium is 



the difference of potential between the conductor and the sheath 



and therefore the charge per centimeter is 



9 = -^; (61) 



210*1 



the potential of P is 



and substituting for q its value from equation 61, 



(62) 



this equation is plotted in curve 1, Fig. 33, and represents the 

 potential at all points between the conductor and sheath. The 

 potential gradient or electrostatic stress in the medium at the 

 point P is 



9/> T? 



(63) 



and varies inversely as the distance from the centre of the con- 

 ductor. Its values are plotted in curve 2. 



The stresses in the dielectric are not uniform, but are greatest 

 near the conductor and least in the outer layers near the sheath. 

 The outer portion of the dielectric is therefore not used to the 

 best advantage. 



