60 L. Page — Fundamental Relations of Electrodynamics. 



v x > v, - ;; [ v. v x - v x v.] 



and similarly for Y y 



V' V, 



o-^r ('■-?■)■ 



Moving Charges. 



We cau represent the field due to a charged particle which 

 is at rest relative to the observer by radial lines of force so 

 drawn that equal solid angles contain the same number of lines 

 of force. Then we can define the intensity at any point as 

 having the direction of the line of force at that point and as 



Fig. 1. 



being proportional, in magnitude, to the density of the lines of 

 force at that point. Now let us extend this definition of 

 intensity to charges which are moving relative to the observer. 

 Consider a charge e at' the point O' (fig. 1) in K (v). Let 

 dS' be an elementary surface fixed in K (v) at P', and perpen- 

 dicular to O'P'. Let O'P' — r ', and the angle between O'P' 

 and the Z' axis be 6'. Then E', the force at P' as measured 



in K (v), will be -^. We wish to find the force E due to e, 



at a point P in K (o), when P coincides with P'. On account 

 of the different definitions of simultaneity in the two systems 

 K (v) and K (o), when P' and P coincide the charge e as viewed 

 from K (o) will be at some point O not coincident with O'. 

 Let OP = r, and let the angle between OP and the Z axis be 6. 

 The space time transformations give the relations 



