Page:Elementary Text-book of Physics (Anthony, 1897).djvu/306

293 position of other conductors in the field. When the charged conductor is in very close proximity to another conductor which is kept at zero potential, the amount of charge needed to raise it to unit potential is very great as compared with that required when the other conductor is more remote. Such an arrangement is called a condenser. If the charge on a conductor be increased, the increase in potential is directly as that of the charge. Hence the capacity $$C$$ is obtained by dividing any given charge on a conductor by the potential of the conductor, or The practical unit of capacity is the farad, which is the capacity of a conductor, the charge on which is one coulomb (§ 255) when its potential is one volt (§ 303). This unit is too great for convenient use. Instead of it a microfarad, or the one-millionth part of a farad, is usually employed.

The equation gives the dimensions of capacity. Measured in electrostatic units, they are $$[C] = \left[ \frac{Q}{V} \right] = \frac{M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-1}}{M^{\frac{1}{2}}L^{\frac{1}{2}}T^{-1}} = L.$$

258. Specific Inductive Capacity.—The capacity of a condenser of given dimensions depends upon the insulating medium used to separate its parts, or the dielectric. This was first discovered by Cavendish, and afterwards rediscovered by Faraday. If $$Q$$ represent the charge required to raise a condenser in which the dielectric is vacuum to a potential $$V,$$ then if another dielectric be substituted for vacuum, it is found that a different charge $$Q'$$ is required to raise the potential to $$V.$$ The ratio $$\frac{Q'}{Q} = K$$ is called the specific inductive capacity, or dielectric constant. Since $$C' = \frac{Q'}{V}$$ and $$C = \frac{Q}{V}$$ are the capacities of the condenser with the two dielectrics, it follows that where $$C$$ is the capacity with vacuum as the dielectric. The specific