MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 163 



The components of electric force at r = a, are 



e(l-k 2 )x 2f ekCtx(a 2 -x*) ex 2 i k 2 E \ 



~ a a 2 -k 2 x 2 C 2 a a*-kW G 2 a a 2 -k 2 x 2 \ ' h 1 -W 



ey 2f ekCtx !1 y fexy f 



* -* * - * 2 - 2 * -- 2 ' 



a (a* -Pa*) C*a (tf-tfxj C*a (a 2 -k 2 x*) (1 -A,- 2 ) V ' 1 -tfj ' 



\ 

 1 / 



7 _ cz 2f ) ekCtx 2 z exz / FB\ 



aa 2 -k 2 x* CV-A-'V 2 C 2 aa 2 -Vl-/; 2 \ I-*' 



Thus the surface density of electricity is given by 



e fl 



= + 



There is thus a redistribution on the sphere while the total charge remains 

 unaltered. 



The mechanical reaction on the sphere in the direction of x is ^JcrX' dS, since in 

 this case there is no surface current, and X' = X. 



The term in f t vanishes on integration, and hence, neglecting squares of jf u , the 

 value is 



Hence the equation of motion is 



Thus a uniformly accelerated motion is possible, and the initial electric inertia for 

 longitudinal acceleration is 



<'* f ' 2 1 i (l+A)l 



J [no- \ ' V 



aC 2 lFl.-F F n l-A;)i 



This result is the same as that of ABRAHAM for a rigidly electrified sphere. The 

 investigation shows, however, that a redistribution of the charge takes place. 



The limiting value of the expression for k = is |e 2 /aC 2 . 



6. Initial Motion of a Charged Conducting Sphere moving with any Speed after 

 Transverse Acceleration is imposed. The sphere being in steady motion with velocity 

 &C parallel to x, we now suppose the accelerating force to act at right angles to the 

 original direction of motion. 



Thus we now take f (t) as a small displacement parallel to the direction of y. 



Y 2 



