178 ADVANCED ELECTRICITY AND MAGNETISM. 



2* - ( 4) 



where V is the electric potential in volts at a point r centimeters 

 from a line charge of Q coulombs per centimeter, and B = 

 1.131 X io 13 . 



It is evident that V is a constant for any given value of r, 

 and therefore the surface of any circular cylinder with its axis 

 along A is an equi-potential surface. The circles in the 

 upper part of Fig. 116 represent a series of equipotential sur- 

 faces. 



Distribution of electric potential in the neighborhood of two 

 parallel equal and opposite line charges. Figure 1 17 is a sectional 

 view of two parallel line charges, + Q and - Q coulombs per 



centimeter respectively. The 

 potential at p due to + Q 

 alone is given by writing r\ 

 for r in equation (4) , and the 

 potential at p due to - Q 

 alone is given by writing 

 Q for Q and r z for r in 

 equation (4); and the total 



potential at p due to both line charges is the algebraic sum of 

 the expressions so found. Therefore: 



~ \ 



(5) 



For a series of constant values of V this equation becomes 

 the equation of a series of circles as shown in Fig. 118. These 

 circles represent a series of cylindrical surfaces at right angles 

 to the plane of the paper. These cylindrical surfaces are equi- 

 potential surfaces. The lines of force of the electric field due to 

 two parallel equal and opposite line charges are shown in Fig. 

 119. These lines of force cut the equipotential surfaces at right 

 angles as shown in Fig. 112. 



