Page:Elementary Text-book of Physics (Anthony, 1897).djvu/307

§ 259] inductive capacity $$K$$ is always greater than unity. Some dielectrics, such as glass and hard rubber, have a high specific inductive capacity, and at the same time are capable of resisting the strain put upon them by the electric stress to a much greater extent than such dielectrics as air. They are therefore used as dielectrics in the construction of condensers.

259. Condensers.—The simplest condenser, one which admits of the direct calculation of its capacity, and from which the capacities of many other condensers may be approximately calculated or inferred, consists of a conducting sphere surrounded by another hollow concentric conducting sphere which is kept always at zero potential by a ground connection. For convenience we assume the specific inductive capacity of the dielectric separating the spheres to be unity. Let the radius of the Fig. 79. small sphere (Fig- 79) be denoted by $$R,$$ that of the inner spherical surface of the larger one by $$R';$$ let a charge $$Q$$ be given to the inner sphere by means of a conducting wire passing through an opening in the outer sphere, which may be so small as to be negligible. This charge $$Q$$ will induce on the outer sphere an equal and opposite charge, $$-Q.$$ Since the distribution on the surface of the spheres may be assumed uniform, the potential at the centre of the two spheres, due to the charge on the inner one, is $$\frac{Q}{R},$$ and the potential due to the charge of the outer sphere is $$-\frac{Q}{R'}\cdot$$ Hence the actual potential $$V$$ at the Centre, due to both charges, is $$\frac{Q}{R} - \frac{Q}{R'} = Q \left( \frac{R' - R}{RR'} \right) \cdot$$ Hence the capacity is In order to find the effect of a variation of the value of $$R,$$