506 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



example in the case of a circular ring placed perpendicularly to the 

 force of a varying uniform magnetic field the electric potential is 

 constant. If however the circuit is broken, current flows for a 

 very short time until the electric force vanishes; there is then 

 produced a disturbance of charges producing differences of 

 potential to be calculated from the equations 



_a_F = ap _aF_a _^_T_^ 



dx~~dt' dy ~ dt ' dz~~dt' 



Conductors connected to the broken ends of the circuit, for 

 instance the plates of an electrometer, will then show a difference 

 of potential. 



244. Displacement Currents. If we compare the equa- 

 tions (5) with the equations 222 (2), 



= -- -5 , 



oy oz 

 dL dN 



dM dL 



4-7TW = - -- , 



06 oy 



we notice that they are analogous in having the right-hand sides 

 equal to the curl of the electric and magnetic field respectively. 

 We make the analogy still more complete by introducing the 

 conception introduced into the theory by Maxwell of the electrical 

 displacement current *. 



Suppose that we have a condenser charged with electricity. 

 There is then a field of electric force, the lines of force running 

 from the positively charged plate to the negative. The electric 

 induction is, by 182 (i 6), 



g = 47TCT. 



If now the plates be connected by a conducting wire, the 

 positive charge passes from the positive plate along the wire, until 

 a state of equilibrium is reached. During this period the electric 

 induction between the condenser plates is diminishing and finally 

 reaches zero. The hypothesis of Maxwell is that the change of the 



* "A Dynamical Theory of the Electromagnetic Field (11)," Phil Trans. Vol. 

 CLV. 1864. 



