243, 244] EQUATIONS OF ELECTROMAGNETIC FIELD. 507 



induction produces the same magnetic effect as would be produced 

 by a current of current-density 



at every point of the field, which together with the current in the 

 wire would form a closed circuit. As the equations 222 (2) were 

 deduced from the magnetic effect of closed currents, some hy- 

 pothesis is necessary if we are to deal with unclosed currents, and 

 Maxwell's hypothesis is justified by its remarkable consequences. 

 Since Maxwell calls the vector g/4?r the electrical displacement, he 



1 ?f% 

 terms the vector the displacement current. 



The consequence of Maxwell's hypothesis is that in the dielec- 

 tric we must introduce the components of the displacement 

 1 83P 1 8g) 1 33 . , 



m the 

 tions ( 1 1 ), giving 



d$ == dN_dM >B ^e*AAlH 



dt 'by dz ' 



dVjL_dN ?*. 



dt dz dx ' 



dj$ = dM_dL 



dt dx dy ' 



These equations are now completely analogous to the equations 

 (5) except for the difference of sign on the left, the two sets being 

 represented by 



(13) 



If the dielectric is conducting, we must introduce both the 

 conduction and the displacement current, so that the equations are 



8 8^ dM 



^r + 4nrw = ^- -^ , 

 dt dy dz 



8g) , dL dX 



(14) -^ -- -, 



dt dz dx 



83^ dM dL 



+ 4<7rw=- -- . 

 dt dx dy 



