ELECTRICAL CAPACITY. 59 



72. ELECTRICAL CAPACITY. We have designated as the capacity 

 of a conductor the charge which must be given to it to raise it to unit 

 potential, when all the conductors which surround it are in communi- 

 cation with the earth. 



It follows, from this definition, that the capacity of a conductor 

 depends not merely on its own shape, but on the shape and position 

 of the conductors which surround it. 



We shall represent this constant by the letter C. If, while the 

 conditions remain the same, a charge M is imparted to the con- 

 ductor, in virtue of the principle of superposition of conditions of 

 equilibrium, its potential will be 



from which follows 



M = CV. 



The problem of determining the capacity of a conductor in a 

 given case, amounts to investigating the state of equilibrium of the 

 system formed of the conductor in question, together with those 

 surrounding it, these latter being in connection with the earth; it 

 merges then into the general problem of equilibrium. 



The word capacity has been borrowed by analogy from the 

 theory of heat ; but it is important to remark that while the calorific 

 capacity of a body only depends on the nature and weight of the 

 body, the electrical capacity of a conductor depends neither on its 

 nature nor on its weight, but solely on its external shape and on the 

 shape and position of all the adjacent conductors. The electrical 

 capacity is not therefore a constant, fixed for the body in question, 

 as is the thermal capacity. 



73. SPHERE. Let us consider a conducting sphere at a great 

 distance from any other conductor. Let R be its radius, M its 

 charge. By symmetry this charge forms a uniform layer on the 

 surface ; it satisfies, moreover, the condition of equilibrium, for its 

 action on any internal point is null (42). The potential is, therefore, 

 constant throughout the whole interior; its value at the centre is 

 M 

 - ; hence, 



V = ^ or M = RV. 

 -R 



The capacity of the sphere is, therefore, 



C = R; 



