Page:Electricity (1912) Kapp.djvu/78

74 of a very large room, in which the sphere is suspended, is not necessary to our arguments. We may reduce the room to any extent, and still the definition of potential, or, as we now see, that of e.m.f., holds good. It is the energy required to carry unit positive charge from the wall to the sphere. Since there is no restriction to the size of the room, other than there must not be actual contact between wall and sphere, let the room shrink until it has become merely a spherical shell surrounding the sphere closely, the distance being a very small length $$\delta$$. Let this be a mere clearance space, so small in comparison with the radius of the sphere that the repelling force of the charge $$Q$$ on our unit has sensibly the same value at any point within this very narrow space. The repelling force is

and since the product of force and distance traversed is energy, we find

and

instead of $$eR$$ as found previously, when the