Reprint of papers on electrostatics and magnetism . find qh(f-h) < PQ , _,rPQ ~\ \ ,«.. ^-^^ ^^ L^vpz:pzJ; ^^^ for the electric density on the side of B remote from Q (that is,the convex or concave side, when B is spherical, according as Qis within or without the completed spherical surface). Theelectric density on the side next Q is [§ 241 (20)] the same,with the addition of ^^,(/_^) ^ ^ These formulae, (25) and (26), express the electric density onthe two sides of a circT^lar segment or disc of infinitely thinspherical or plane conducting surface conne
Reprint of papers on electrostatics and magnetism . find qh(f-h) < PQ , _,rPQ ~\ \ ,«.. ^-^^ ^^ L^vpz:pzJ; ^^^ for the electric density on the side of B remote from Q (that is,the convex or concave side, when B is spherical, according as Qis within or without the completed spherical surface). Theelectric density on the side next Q is [§ 241 (20)] the same,with the addition of ^^,(/_^) ^ ^ These formulae, (25) and (26), express the electric density onthe two sides of a circT^lar segment or disc of infinitely thinspherical or plane conducting surface connected with the earthby an infinitely fine wire, and electrified by the influence of aquantity — q oi electricity insulated at a point Q anywhere inits neighbourhood. 244. The position of the auxiliary point D (which appears inthe diagrams as the image of D, the unoccupied pole of the lipof the original bowl S) may be found, without reference to 8,by construction from 8 and Q supposed given; thus :—From(22) of § 243 we have KD:DL::KQ:QL (27),. XV.] Segment of Spherical Gondvxting Surface. 189 where Z and i may be tlie points in which, the lip of the bowl S is cut by any plane through QDD. Let, for instance, this plane pass through the centre of one of the spherical surfaces. It must also pass through the centre of the other, and bisect each bowl; and \i E, F be the points in which ,,-- --v^ j^ it cuts the lip of S, (2 6) applied to the present case gives (Euclid, vi. 3)the lines bisecting the angles EDF, EQF cut ^--., ,„. the base EF in the same point; and D must be in the circle which is the locusof all points in the plane EFQ fulfilling this condition, beingfound by the well-known construction, thus :—Bisect the angleEQG by QA, meeting EF in A. Draw QB perpendicular toQA, and let it meet EF produced, in B. On BA as diameterdescribe a circle, which is the required locus; and D is thepoint in which this circle cuts the unoccupied part of thespheric
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectmagnetism, bookyear18
