Electricity for public schools and colleges . true for any surface, p being the density at the pointconsidered. This general result is, in more advanced Courses, provedindependently, without reference to a sphere. § 25. Important Case of a Spherical Condenser.—We willnow show how to find the capacity of a spherical condenser. As in the case of an isolated sphere we found hio expressionsfor the potential of the sphere, and by equating them found thecapacity of the sphere ; so here, in thecase of two spherical surfaces forming acondenser, we shall find two expressionsfor the difference of potent
Electricity for public schools and colleges . true for any surface, p being the density at the pointconsidered. This general result is, in more advanced Courses, provedindependently, without reference to a sphere. § 25. Important Case of a Spherical Condenser.—We willnow show how to find the capacity of a spherical condenser. As in the case of an isolated sphere we found hio expressionsfor the potential of the sphere, and by equating them found thecapacity of the sphere ; so here, in thecase of two spherical surfaces forming acondenser, we shall find two expressionsfor the difference of potentials of the twosurfaces, and then by equating them shallfind an expression for the capacity of thecondenser. The figure represents the idealspherical condenser, in which there aretwo concentric spherical conductors, theinner being totally enclosed by the outer. In the practical con-denser we must have an opening through the outer conductor,and an insulated wire and knob connected with the mner; as inFaradays condenser. Chapter IX. § 4. L. 146 ELECTRICITY ch. x. Let C be the centre. Let the radius of the inner conductorbe Ra cms., and the charge on it be + Q ; then there will be onthe inside surface of the outer conductor a charge of — Q, byChapter IV. § 16. Let the inner radius of this outer conductorbe Rb cms., and its outer radius be r cms.; and let there be on theouter surface of B a charge Q. As we wish to find an expression for the diiTerence of potential(Va — Vb) between the two surfaces, we will find V^ and Vg sepa-rately first. The reader must note that Q is the boimd charge ofChapter VI. Now Va is the potential of any point on, or in, A, since A isa conductor containing no insulated charged bodies ; and, there-fore, Va is the potential at C. Hence V^ = ^ + ^ + 5-Ra Rb r by the results of § 19. And Vb will be the same as the potential of a point just on the outer surface of B. But, by § 17 (4), this will be the same as that which would be due to all the charg
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