338 Motion of Electrification through a Dielectric. 



let q be the surface density, 

 and the plane be moving 

 perpendicularly to itself. 

 Let it be of finite breadth 

 and of infinite length, so 

 that we may calculate H 

 from (43). The result at 

 Pis 



H- g^ iQ^ n^-3/>7^' /44X 



When P is equidistant from the edges, H is zero. There is 

 therefore no H anywhere due to the motion of an infinitely 

 large uniformly charged plane perpendicularly to itself. The 

 displacement-current is the negative of the convection- 

 current and at the same place, viz. the moving plane, so 

 there is no true current. 



Calculating E^, the ^-component of E, z being measured 

 from left to right, we find 



cE. = 2,(tan-'^^(l-^')*-tan-.f(l-''')'}.(45) 



The component parallel to the plane is H/cm. Thus, when 

 the plane is infinite, this component vanishes with H , and 

 we are left with 



cEi = cE = 27r^, (46) 



the same as if the plane were at rest. 



19. Lastly, let the charged plane be moving in its own 

 plane. Refer to the first figure, in which let AB now be the 

 trace of the plane when of finite breadth. We shall find that 



H = 2gu[tan- ^^^_;,^^,y ]]' . . . (47) 



zi and Sg being the extreme values of z, which is measured 

 parallel to the breadth of the plane. 



Therefore, when the plane extends infinitely both ways, we 

 have 



H = 27r^M (48) 



above the plane, and its negative below it. This diff'ers from 

 the previous case of vanishing displacement-current. There 

 is H, and the convection-current is not now cancelled by co- 

 existent displacement-current. 



The existence of displacement-current, or changing dis- 

 placement, was the basis of the conclusion that moving elec- 

 trification constitutes a part of the true current. Now in the 



