Reprint of papers on electrostatics and magnetism . y uniformly distributed over asurface of infinite extent, and will therefore produce no effect;and the same results will be obtained whether we deducethem from the case of an external or of an internal sphericalsurface. 107. Let M be an electrical point possessing a quantity m ofelectricity placed in the neighbourhood of a conductor boundedon the side next jlf by a plane LUwhich we must conceive to be indefi-nitely extended in every direction; itis required to determine the electricaldensity at any point E of the conduct-ing surface. Draw MA
Reprint of papers on electrostatics and magnetism . y uniformly distributed over asurface of infinite extent, and will therefore produce no effect;and the same results will be obtained whether we deducethem from the case of an external or of an internal sphericalsurface. 107. Let M be an electrical point possessing a quantity m ofelectricity placed in the neighbourhood of a conductor boundedon the side next jlf by a plane LUwhich we must conceive to be indefi-nitely extended in every direction; itis required to determine the electricaldensity at any point E of the conduct-ing surface. Draw MA perpendicular to theplane, and let its leng-th be denotedby p. We may, in the first place,conceive that instead of the plane sur-face we have a spherical conductingsurface entirely enclosing the air inwhich M is insulated; and, suppos-ing the shortest line from M to thespherical surface to be equal to p, we should have, according tothe notation of § 103, f=a—p. Hence the expression (A) becomes _ ^2ap—p^ m _ Ip p^ \ m^~ iira ME^~ ~~\2tt~^im)ME. 74 On the Mathematical Theory of Mectricity. [v. In this, let a be supposed to be iufinitely great; the secondterm within the vinculum will vanish, and we shall have simply p= ^^P- (A) for the required electrical density at the point E of the in-finite plane electrified inductively through the influence of thepoint M. CoE. The total amount of the electricity produced by in-duction is equal in quantity, but opposite in kind, to that ofthe influencing point M. We have seen already that the sameproposition is true for internal spherical surfacesinductively electrified; but it does not hold for an externalspherical surface, even if we neglect the supplementarydistribution, as it appears from the demonstration of § 92,that the amount of the distribution expressed by the firstterm (that which varies inversely as the cube of the distancefrom the influencing point) of the value of p in equation (J.) of § 93, is equal to —-m. T
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