Page:Electricity (1912) Kapp.djvu/74

70 sphere. The wall of the room being in contact with the earth, both must be considered as at the same potential, and if we arbitrarily fix this as zero (which is evidently permissible since we deal with potential differences and may take our datum line where we like), then the energy expended is the absolute potential of the sphere. We may also now drop the conception of an immensely large room, and assume the sphere suspended in a room of any size, or even in the open. This does not mean that it will in all cases be equally easy to give the sphere the same charge $$Q$$ irrespective of the surroundings; but it means that for the same charge $$Q$$ the potential on the surface will be the same whatever the surroundings may be. Thus we may imagine the sphere charged in the room to the potential

$$V = \frac{Q}{R}$$

If now we knock down the walls, or carry the sphere into another room or into the open, there will be no change in its potential provided that we can avoid loss of charge by dispersion. Now how are we to give the charge $$Q$$ to our sphere? We cannot pick