468 



EXPLORATION GEOPHYSICS 



erning the current distribution in an infinite or semi-infinite conductor. 

 Let E represent the potential difference between two points at which the 

 potentials are Vi and Vo ', then 



Also, the elementary Ohm's law becomes 



. {V2-Vi)A 

 pL 



(1) 



-AVVNA?- 



H7> 



HII 



1—^-1 



..0..J 



Fig. 278. — Circuit illustrating how Ohm's 

 law may be used to determine the resistance 

 by measuring the voltage drop across any 

 known length L of a conductor of uniform 

 area. 



^ 



This law gives the magnitude of the current in a conductor of cross section 

 A sq. cm., length L cm., and resistivity p ohm-cm. when a potential dif- 

 ference of (Fo — Fi) volts exist be- 

 tween the ends of the conductor. 



Differential Form of Ohnv's Law 



Ohm's law can be used to give 

 the value of current which flows be- 

 tween two normal cross sections 

 such as Q and P at an infinitesimal 

 distance dL apart. (Figure 279.) It 

 is assumed that the value of the potential is the same at any point on a 

 cross section normal to the axis of the parallelopiped ; i.e., the normal cross 

 sections are assumed to be equipotential surfaces. If a difference of poten- 

 tial dV exists between the equipotentials Q and P, Ohm's law states that 



Fig. 279 — Homogeneous parallelopiped. Normal 

 cross sections P and Q are equipotential surfaces. 



7 = -^ 



dV_ 

 dL 



