336 Steady Currents in continuous Media [CH. x 



380. As an example of refraction of lines of current flow, we may 

 consider the case of a steady uniform current in a conductor being disturbed 

 by the presence of a sphere of different metal inside the conductor. The 

 lines shewn in fig. 78 will represent the lines of flow if the specific 

 resistance of the sphere is less than that of the main conductor. The lines 

 of flow tend to crowd into the sphere, this being the better conductor in 

 the language of popular science, the current tends to take the path of least 

 resistance. 



Charge on a Surface of Discontinuity. 



381. If u is the normal component of current flowing across the 

 boundary between two different conductors, we have by Ohm's law, 



_! ?EL -- ?? 



TI dn T 2 dn ' 



where =- denotes differentiation along the normal which is drawn in the 

 dn 



direction in which u is measured (say from (1) to (2)), and V lt V 2 are the 

 potentials in the two conductors. 



If there is no charge on the boundary between the two conductors we 

 must, from equation (70), have the relation 



where K l} K 2 are the inductive capacities of the two conductors. This 

 condition will, however, in general be inconsistent with the condition which, 

 as we have just seen, is made necessary by the continuity of u. Thus there 

 will in general be a surface charge on the boundary between two conductors 

 of different materials. 



The amount of this charge is given at once by equation (72), p. 125. If a 

 denotes the surface density at any point, we have 



^-(K^-K^u ..................... (313). 



This surface charge is very small compared with the charges which occur in statical 

 electricity. For instance, if we have current of 100 amperes per sq. cm. passing from one 

 metallic conductor to another, we take in formula (313), 



u=lOO amperes =3 x 10 11 electrostatic units, 

 10-6 



the last two being true as regards ordef of magnitude only. The value of 47r<r is of the 

 order of magnitude of KTU, or ^ x 10 ~ 6 in electrostatic units. As has been said, the value 

 of 47TO- at the surface of a conductor charged as highly as possible in air is of the order 

 of 100. 



