POTENTIAL AND CAPACITY 



81 



the course of the lines of force. This justifies the use of such 

 a plate in the measurement of strain at a point. 



In practice no plate is infinitely thin. A real proof plane will 

 therefore produce some slight modifica- 

 tion of the surrounding field, especially 

 near the edges, where the lines must 

 turn inwards, somewhat as in Fig. 64, 

 to enable some of them to meet the 

 edge normally. 



Capacity of a conductor. If 

 the potential of one conductor of a 

 in is raised while all the rest are 

 kept at zero- potential, as the charge 

 rises in value the induced opposite 

 charges rise in proportion. Hence 



*, or the potential at any point, rises in 



the same proportion. Thus the ratio of 



the charge on the conductor to its potential is constant and is termed 



the capacity of the conductor. We have then this definition : 



If a conductor receives a charge Q and is raised thereby to 

 potential V, while the surrounding conductors are at zero-potential, 



~ is constant, and is termed the capacity of the conductor. It 



is usually denoted by C. 



Sphere in the middle of a large room. Suppose a sphere 

 radius a to receive a charge -f- Q. Let the sphere be placed insulated 

 in a room and let its distance from the walls be great compared 

 with its radium The potential of the sphere will be uniform 

 throughout, and therefore we may find it by calculating the 



FIG. 64. 



potential at the centre. In the formula V 



the positive 



elements are all at the same distance from the centre, and therefore 

 contribute Q/a. The negative elements arc all at a great distance, 



and the sum of the terms 2 is negligible in comparison with Q/a. 

 We have then 



The capacity is 



C = * = a. 



Since the potential at the surface of the sphere has everywhere the 

 same value as that at the centre, viz. : , and is due to the dis- 

 tribution on the surface, the wall charges having negligible effect, 



p 



