14 ELECTRICAL ENGINEERING 



Midway between the spheres the potential is 



-1. -A_- = 

 D/2 D - D/2 



At the surface of A it is 



Q 



R D-R 



(16) 



The potentials at all points between A and B are plotted in curve 

 1 (Fig. 11). 

 The potential gradient at P is 



Midway between the spheres the potential gradient is 



/ Q Q \_ _8Q ( 



UZ)/2)^(D/2)V " # 2 ' 

 which is its minimum value and at the surface of either sphere it 



Z 2 (D - R)*' ...... 



its maximum value. 



The potential gradient is plotted in curve 2, Fig. 11. 



(c) Determine the potential and potential gradient at every 

 point between two parallel cylindrical wires A and B, Fig. 12, 

 of radius R, suspended in air with a distance of D cm. between 

 centers and charged respectively with + q and q units of 

 electricity per centimeter length. 



The electrostatic force at any point P distant r cm. from A and 

 D r cm. from B is the resultant of the forces exerted by the 

 charges on A and B considered as acting independently. 



From each centimeter length of A, 4 TH? lines of dielectric flux 

 extend out normally and produce at the point P a flux density 



2) A = jr -^ = lines per square centimeter. . . (20) 



r 

 The electrostatic force at the point P is 







A = S>A =-^ dynes, (21) 



and acts from A to B. 



