CHAPTER IX. 



STEADY CURRENTS IN LINEAR CONDUCTORS. 



PHYSICAL PRINCIPLES. 



338. IF two conductors charged with electricity to different potentials 

 are connected by a conducting wire, we know that a flow of electricity will 

 take place along the wire. This flow will tend to equalise the potentials of 

 the two conductors, and when these potentials become equal the flow of 

 electricity will cease. If we had some means by which the charges on the 

 conductors could be replenished as quickly as they were carried away by 

 conduction through the wire, then the current would never cease. The 

 conductors would remain permanently at different potentials, and there 

 would be a steady flow of electricity from one to the other. Means are 

 known by which two conductors can be kept permanently at different poten- 

 tials, so that a steady flow of electricity takes place through any conductor 

 or conductors joining them. We accordingly have to discuss the mathe- 

 matical theory of such currents of electricity. 



We shall begin by the consideration of the flow of electricity in linear 

 conductors, by a linear conductor being meant one which has a definite 

 cross-section at every point. The commonest instance of a linear conductor 

 is a wire. 



339. DEFINITION. The strength of a current at any point in a wire or 

 other linear conductor, is measured by the number of units of electricity which 

 flow across any cross-section of the conductor per unit time. 



If the units of electricity are measured in Electrostatic Units, then the 

 current also will be measured in Electrostatic Units. These, however, as will 

 be explained later, are not the units in which currents are usually measured 

 in practice. 



Let P, Q be two cross-sections of a linear conductor in which a steady 

 current is flowing, and let us suppose that no other conductors touch this 

 conductor between P and Q. Then, since the current is, by hypothesis, 

 steady, there must be no accumulation of electricity in the region of the 



