Reprint of papers on electrostatics and magnetism . onducting surface beinsulated or not; and it is impossible to charge this internalsurface initially, or to charge it at all, independently of theinfluence of electrified bodies within it. With the modificationsand omissions necessary on this account, the preceding investi-gations are applicable to the case now to be considered. 103. Peob. To find the electrical density at any point of aninternal spherical conducting surface with an electrical pointinsulated within it. v.] Geometrical Investigations regarding Spherical Conductors. 71 Let m den
Reprint of papers on electrostatics and magnetism . onducting surface beinsulated or not; and it is impossible to charge this internalsurface initially, or to charge it at all, independently of theinfluence of electrified bodies within it. With the modificationsand omissions necessary on this account, the preceding investi-gations are applicable to the case now to be considered. 103. Peob. To find the electrical density at any point of aninternal spherical conducting surface with an electrical pointinsulated within it. v.] Geometrical Investigations regarding Spherical Conductors. 71 Let m denote the quantity of electricity in the electricalpoint Jf; / its distance from G thecentre of the sphere, and a the radiusof the sphere. If the expression for the electricaldensity at any point E of the internalsurface be A. * (A, a constant); the force exerted by the electrified sphericalsurface on any point without it will (§ 90) be the same as if a quantity of matter equal to ^_ ^ were collected at the pointM. Hence if we take X such that XAwa. a-r the total resultant force, due to the given electrical point andto the electrified surface, will vanish at every point external tothe spherical surface, and consequently at every point withinthe substance of the conductor; so that the condition of electricalequilibrium (§ 72), in the prescribed circumstances, is conclude, therefore, that the required density at any pointE, of the internal spherical surface is given by the equation This solution of the problem is complete, since it satisfiesall the conditions that can possibly be prescribed, and it isunique, as foUows from the general Theorem referred to in § * We cannot here, as in [a) of § 93, annex a constant term, since in thiscase there would result a force due to a corresponding quantity of electricity,concentrated at the centre of the sphere on all points of the conducting mass. t For if there were two distinct solutions there would be two different d
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