16516*7] STEADY FLOW IN CONDUCTORS. 



vector qtoE plus the difference of potential between two equi- 

 potential surfaces depends only on the physical properties of the 

 substance in the tube. This is the usual form of the statement of 

 Ohm's Law, and is the integral form, whereas our previous state- 

 ment was the differential form. In the case of electrical flow, 

 the difference of potential V A - V B is called the external 

 or electrostatic electromotive force from A to B, and it is 

 evidently the line integral of electrostatic force along any line 

 from A to B. E is called the impressed, intrinsic, or internal 

 electromotive force. The ratio C of current to total electromotive 

 force is called the conductance of the tube. Its reciprocal R is 

 called the resistance of the tube. 



If we consider a closed tube of flow, the two surfaces A and B 

 will coincide, and we shall have the ordinary expression of Ohm's 

 Law, 



or: For any closed tube of flow, the current is equal to the 

 impressed electromotive force divided by the resistance of the 

 tube. 



167. Heat developed in Conductors. We shall now con- 

 sider the physical meaning of the integral J in the case of elec- 

 trical flow. In passing from a point where the potential is V A to 

 one where it is V B a unit of electricity does V A V B units of work, 

 and that quantity of electrostatic energy thus disappears. Also at 

 every surface of discontinuity, E r r+l units of work must be done 

 upon it. But if we consider heat as a form of energy, if 

 mechanical energy disappears, an equivalent amount of heat must 

 make its appearance. If accordingly we find energy appearing in 

 no other form, the electrostatic energy W that disappears, to- 

 gether with the work done by the impressed electromotive forces, 

 must be converted into heat. In the case of steady flow we find 

 this to be the case. 



In unit time the quantity 



I = llq cos (qn) dS 



crosses any section of a tube of flow, so that considering that part 

 of the conductor between the equipotential surfaces A and B we 



