9* STATIC ELECTRICITY 



Practical methods of measuring potential. If the 

 centre of a conducting sphere is brought to the point at which the 

 potential V is required and is then connected to the zero-level 

 surface, say the earth, by a wire, its potential becomes zero. Let 

 Q be the charge induced upon it. The potential at the centre of 

 the sphere being zero, we have 



22 = 0. 



r 



But, if the wire is exceedingly fine and if the sphere is sufficiently 

 small, this may be split up into the terms due to the original 

 electrification practically undisturbed by the introduction of the 

 sphere and giving value V, and the terms due to the charge gathering 



on the sphere and giving value . Then 





On breaking the earth connection and taking the sphere away, it 

 we measure its charge, we obtain a number proportional to tin- 

 potential at the point, though opposite in .sign. A very obvious 

 weakness in this method lies in the neglect of the charge on the 

 connecting wire. It is not easy to make the capacity of the win- 

 negligible in comparison with that of the sphere. 



Reduction of the potential of a conductor to that of a 

 given point in air. Suppose, for example, that we wi>h to 

 equalise the potential of a pair of the quadrants of a quadrant 

 electrometer to the potential of a given point P, Fig. 68, in the air. 



Suppose, to begin with, that they are at 

 higher potential. Take an insulated wire 

 from the electrometer to the point 1* : 

 the end of the wire is evidently at higher 

 |p\ potential than its surroundings. Thru 

 \ it is positively electrified, while the quad- 

 . - - ) rants are negatively electrified. Imagine 

 V J now that the outer layer of the wire is 



^JL^ loose, so that it can be drawn of}' into the 

 FIG. 68. air with the charge on it. The poten- 



tial of the wire at P is thereby lowered 



more nearly to that of the air near it. A new positive charge will 

 now gather at P and more negative will go into the quadrat 

 If the new surface is also loose, the new charge will also be drawn 

 oft' into the air, and if we so imagine successive layers to be 

 removed they will carry with them positive charges until the end 



