4.— THE TKEArMEN'r OF ELECTRODYNAMICS. 



}\y \\. A. I.KUKKLDI', D.Sc'. 



It lias \o\vj, been custoniaiy in English Ixioks to treat magnetism 

 Vjefore current electrioit}', and "explain" the latter by analogy ^witli 

 the action of magnetic shells. This mode of presentation has always 

 seemed to the writer unsatisfactory, putting the more obscure pheno- 

 menon as an explanation of the simpler; and now that tne electron 

 theory has shown itself capable of application to all brandies of elec- 

 tricity, it is most inappropriate, since magnetism is looked up()n as an 

 effect of molecular electric currents. An attempt has therefore been 

 made to put the treatment of electrodynamics, including magnetism, 

 on a more logical basis. 



The experimental starting-point is the brilliant investigation of 

 Ampere on the forces between conductors canying currents. The 

 electrostatic forces, although out of all proportion greater in amount, 

 produce no eft'ect, on account of the equal quantities of positive and 

 negative electricity in each wire. Again, a charge in motion produces 

 no effect, so far as is known, on a charge at rest. There remain, 

 therefore, only the purely electrodynamic forces — the action of one 

 moving charge on another moving charge. These forces can be ex- 

 plained by means of the concept of a magnetic field, but it is better to 

 begin with the forces themsehes, although their spatial relations are 

 somewjiat complicated. 



Let us suppose, then, a charge '.', located at the origin and )noving 

 with the vector velocity V, whose components are (?<p ?'j, o) ; i.e. the 

 axis of z is chosen perpendicularh' to the motion. Another charge e., 

 is located at the point (r, o, o), and has the velocit}' V., with com- 

 ponents (u.„ IK,, tr.-,). Then the first charge exerts on the second a force 

 F, which has components in the .'.• and i/ directions, but not in c, and 

 its components are 



e^ v-^ e. V , e, 0, e., u, 



i'x- = - 7~r' '^y = + T~> ' 



c- r- 0- r- 



where the charges are expressed in electrostatic units and c is the 

 velocity of light. The reaction exerted by e., on <'^ is not equal and 

 opposite to this, because the momentum of the field must be taken into 

 account if we wish to apply jSewton's laws of )notion. That is of no 

 conse<iuence for the present ]iurpose, however, as the laws just stated 

 enable one to calculate the forces and hence the motions, whether of 

 the conductors as a whole or of the electrical charges within them. 



Now it is of assistance to regard this action as taking place in two 

 stages, and say that the movement of the first charge produces a 

 magnetic field, and that this field acts on the second charge, causing a 

 mechanical force. 



