An Introduction to the Mathematical Theory of Attraction
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An Introduction to the Mathematical Theory of Attraction

An Introduction to the Mathematical Theory of Attraction


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1899 Excerpt: ... surface so as to produce at each point a resultant force normal to the surface, which is therefore an equipotential surface for this distribution, and the electric mass constitutes what is termed a couche de niveau. If the total amount M of mass be given, there is only one possible distribution consistent with electric equilibrium. For, if there be two possible distributions, let their potentials in external space be IT and V; then at the surface 8 of the conductor we have U = d, V = C2; and if v be the normal to 8 drawn outwards, also if x = V-V, by equation (9), Art. 58, is constant throughout the whole of space outside 89 and therefore-is zero at every point of 8; whence the density of the disdv tribution producing V is everywhere the same as that of the distribution producing V. It can be shown, as in Art. 70, that there is only one possible distribution of mass over a closed surface 8 producing a given potential at every point of this surface. Hence, if an insulated conductor be charged to given potential, the quantity and distribution of electricity on its surface is determined. Examples. 1. The potential V is cj (%, y, z) throughout the region inside a closed surface S, and is zero throughout external space; find the corresponding distribution of mass. In order that it should he possible to fulfil the required conditions f (%, y, z) must be zero at the surface S; then inside S, the density p is given by the equation iirp + v2 = 0, and the surface density t on S by the equation 47rc +---= 0, where v is the normal to 8 drawn inwards. Since S is an equipotential surface corresponding to V, we have dv ydx) " dy) + dz) 2. Find the equipotential surfaces of a homogeneous homoeoid in external space. A homoeoid is a couche de niveau, and therefor...


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Product Details
  • ISBN-13: 9781152341555
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 74
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1152341553
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 150 gr


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