230 Mr. J. J. Thomson on the Electric and Magnetic 



§ 2. The first case we shall consider is that of a charged 

 sphere moving through an unlimited space filled with a medium 

 of specific inductive capacity K. 



The charged sphere will produce an electric displacement 

 throughout the field; and as the sphere moves the magnitude 

 of this displacement at any point will vary. Now, according 

 to Maxwell's theory, a variation in the electric displacement 

 produces the same effect as an electric current; and a field in 

 which electric currents exist is a seat of energy; hence the 

 motion of the charged sphere has developed energy, and con- 

 sequently the charged sphere must experience a resistance as 

 it moves through the dielectric. But as the theory of the 

 variation of the electric displacement does not take into account 

 any thing corresponding to resistance in conductors, there can 

 be no dissipation of energy through the medium ; hence the 

 resistance cannot be analogous to an ordinary frictional resist- 

 ance, but must correspond to the resistance theoretically ex- 

 perienced by a solid in moving through a perfect fluid. In 

 other words, it must be equivalent to an increase in the mass 

 of the charged moving sphere, which we now proceed to cal- 

 culate. -A i 



Let a be the radius of the moving sphere, e the charge on 

 the sphere, and let us suppose that the sphere is moving 

 parallel to the axis of x with the velocity p ; let f, 77, f be the 

 coordinates of the centre of the sphere ; let /, g, h be the com- 

 ponents of the electric displacement along the axes of x, y, z 

 respectively at a point whose distance from the centre of the 

 sphere is p, p being greater than a. Then, neglecting the 

 self-induction of the system (since the electromotive forces it 

 produces are small compared with those due to the direct action 

 of the charged sphere), we have 



„__ e d 1 

 * ~~ 47r dx p 



= -i- A 1 



J~ 4=ir dy p 

 j _ _ e d 1 

 47r dz p ' 



therefore 



d£_ _ ep d 2 1 

 dt~ kirdxd^p 

 dg _ _ ep d 2 1 

 dt A.7T d% dy p 



dh_ e d 2 1 % 

 dt~~ Airdtjdzp' 



