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Problems in Electric Convection. 



[Mar. 19, 



tions are called the electric and magnetic convection potentials 

 respectively. 



The conditions which are necessary in order that the electricity 

 may be relatively at rest on any surface on which it is being conveyed 

 are next investigated, and it is shown that it is not the electric force 

 E, but the mechanical force F, which must be normal to the surface. 

 The equilibrium surfaces are therefore given by ^ = constant. The 

 mechanical stress on the moving charged surface has a tangential com- 

 ponent, and for certain directions of the normal may have a normal 

 component inwards, provided that ujv exceeds 0*810465, where u is 

 the velocity of the system and v the velocity of light. 



The energy of a moving electrical system takes the form 

 2T + J2g 1 if p , where T is the total magnetic energy and ^ is the value 

 of the electric " convection potential " at the charge q. 



The ellipsoid of revolution which is given by = constant, where 

 , \f r is the value of the electric u convection potential " for a point- 

 charge moving at the same speed, is called the " Heaviside " ellipsoid. 

 A complete solution is given for the case in which this ellipsoid is 

 electrified and is moving along its axis of figure. At all external points 

 it produces the same effect as a point charge at its centre would do. 



For an ellipsoid of any shape it is shown that the distribution of 

 electricity over its surface is the same whether the ellipsoid be at rest 

 or in motion. 



Finally, a complete solution is given for an ellipsoid of revolution 

 in motion along its axis of figure. If the ellipsoid (a, b, c) is moving 

 along one of its axes (a), the surfaces of equal " convection potential" 

 are given by 



x 2 y 2 z* _ 



a 2 + ^i' t b 2 + \ + c 2 + X ~~ *' 



where a = l—u 2 /v 2 and X is a variable parameter. When h = c the 

 lines of electric force are given by the hyperbolic members of the 

 family of curves given by 



a? + a\ b 2 + X 



where p 2 = y 2 -\-z 2 . 



The ellipsoid produces the same field as either a uniformly charged 

 line or a charged disc placed symmetrically inside the surface, 

 according as the ellipsoid is more prolate or more oblate than Heavi- 

 side's. For a sphere of radius a the length of the line is 2au/v. The 

 energy of the ellipsoid is calculated, and the result for a sphere of 

 radius a carrying a charge q is found to be 



2ica \u v—u J 

 where k is the specific inductive capacity of the medium 



