PLANE SHELL. 559 



576. Let us now investigate the currents in the plate. The 

 component u of the current parallel to the x axis, which intercepts 

 unit length parallel to the y axis, is 



and the component v of the current parallel to the y axis 



If a- be the resistance of the plate for unit surface, the fall of 

 electrical potential for unit length will be <ru parallel to the x axis, 

 and (TV parallel to the y axis ; this fall of potential is but the electro- 

 motive force in the same directions. Hence, from the expressions 

 found above (568), we have for a field variable with the time, 



The equations (2) give, for the positive face, 



27T 



from this follows 



- <)G 



The general equations (567) which connect the components of 

 the total electromotive force of induction with the magnetic 

 potential give, in the present case, 



3G 3H _ DV_ 



^z *by "bx 



