APR A.] CALCULATION OF INERTIA 205 



however, they tend to prolong the current which main- 

 tained them. Consequently, if the moving charge (or 

 current) tries to stop, its retardation meets with 

 obstruction; it is constrained to persist by the sub- 

 sidence of the magnetic field which its motion excited 

 and maintains. Its velocity is not resisted, there is 

 nothing equivalent to friction, but its acceleration + or 

 is obstructed, an effect precisely analogous to inertia. If 

 it is at rest it will need force to start it, and if it is in 

 motion its motion will persist, even against force, for a 

 time. 



The charge acts, therefore, as if it had inertia, and we 

 can proceed to calculate its amount. 



While moving it is a current, and will be surrounded 

 by rings of magnetic force, whose intensity, at any point 

 with polar co-ordinates r, 0, referred to the line of motion 

 as axis and the moving charge as origin, will be the 

 quite ordinary expression (with eu for the current-element 



instead of Cds) . * 



TT eu sin 6 

 ti = - = . 



r 2 



The ordinary expression for the electrostatic force at 

 the same point is 



(see note at end of Chapter I. with reference to the inser- 

 tion of K) and if the motion is slow this value will be 

 preserved; but if it is rapid the electric field gets weaker 

 along the axis and stronger equatorially, having been 

 shown by Mr. Heaviside (Philosophical Magazine, April, 

 1889) to be given by the following expression 



where v is the velocity of light. 



