38 Kepoht 8. a. a. Advanckmkxt of 8cikxci:. 



Calling the magnetic field H, we may define it as a vector of the 

 A'alue 



XT ^1 ^'l 



^z = 7 



pr- 

 ill the direction of z and without components in the other directions, 

 and can then say that the field H acts on the charge e., moving with 

 velocity (?/., v.. ?r.,) with the force components 



„ H e., v., , „ H ^., II., 

 F, = + — '—= and F,. = - ^^ 



H e., . / u.^^ + v^- 



i.e. with a resultant force = perpendicular to the plane 



c 



containing the field and the velocity, and proportional to their vector 

 product. 



The signs occurring in the above equations may be determined by 

 the well-known "right-hand screw'' and "three-finger" rules. 



It is, of course, open to dispute whether the above statements form 

 a complete account of the action of one moving electron on another, 

 since that action is not directly accessible to experiments ; it might be 

 proposed to employ the " rationalised current element," consisting of 

 the system of lines of force produced b}^ a moving electric charge, in 

 addition to the charge itself. But again this is unnecessary here, as 

 we are onh' concerned to find the simplest means of calculating 

 observed efiects of electric currents and magnets. We will therefore 

 take the above rules and apply them to certain cases. 



A conduction current consists in a continu(jus succession of mo^■ing 

 charges. Let there be a short element of wire, of length dl, in which 

 there are on the average n electrons per unit length, each of charge e, 

 and travelling with the average velocity V. Then neY is the total 

 charge conveyed per second across a section of the wire, i.e. the cur- 

 rent, in electrostatic measure. In electrodynamic units the current 



In the short length considered, howe\er, there will ])e ndl electrons, 

 so that the total electrodynamic effect of that length will be propor- 



ne Y dl ^ 



tional to = idl. We may accordingly write the former equa- 



(' 

 tions in a form suitable for conduction currents as : — 



?•- 



F, = + Ki, d/, sin a, Fv = - Hf, dl., cos $, 

 where 0.. is the angle whose tangent is r.^ h- " ... 

 The resultant force is therefore F = Hi., dl... 



