THK INDUCTION OR ELECTRIC STRAIN 53 



electric strain at any point in a medium by the charge per unit area 

 gathering on a conducting surface which is introduced so as to 

 pass through the point, but which does not alter the strain in the 

 region immediately outside itself. 



\Ve shall usually denote the strain by D. The quantity which 

 is here termed electric strain is, as already stated, that which 

 Maxwell termed "electric displace- 

 ment." We have thought the 

 former term preferable as having no 

 meaning beyond that which we put 

 into it. The latter term almost 

 irresistibly carries with it the idea 

 that electric strain is a displacement 



inethin: in tin- direction of in- 

 duction, an idea \\hich may prove a 

 hindrance rather than a help. 



The variation of electric 

 strain with distance from the 

 charged surfaces or bodies. 

 The inverse square law. It a 

 conducting spin i \ 1 iJ.uitHa Fio. 42. 



charm- -f V ' N huiii: bv an insulating 



thread within a hollow spin : ity in a conductor B, the two 



sphrrir.d surface* bt'inij concent i ic, <^) will be induced on the 

 i micr surface of B. If the insulating medium is homogeneous, then 



. s\miii<-tr\ each ch.-r uniformly so that if A and B 



are the radii and <T A TB th I per unit area or surface densities, 



'.' ' 4ra*<r A : - Q = *** 

 when,, VA = J = - 



i tin- strain in tin- medium ju.st outside each surface is from 

 tlu- ml inuTM-lv as the square of the distance from the 



If we suppose the radius ot the outer surface reduced till it 

 panes through a point close to P distant r fiom the centre, the 



strain at 1* is now measured by -7^-5. But there is no reason to 



suppose that the approach of the conductor towards the point 

 has altered the strain in the region between the sphere through P 

 and tin d sphere, for the strain just outside A still remains 



tin saint , \i/,. T-^-J, and it is difficult to imagine this constancy 



;n^ with a variation occurring in the medium a little way off. 

 \V .,; consider that the strain at P is always 7 -j 



so lon as / i- intermediate bet ween / and b. 



bi value tor tli >tr;in uhicli ue should obtain 



