The London, Edinburgh and Dublin philosophical magazine and journal of science . ows. Imagine the circle AEB (fig. 1) replacedby a uniformly charged disk and calculate the repulsion ofthe disk on a unit charge placed at P. This will be mosteasily done by dividing the disk into narrow strips all atright angles to the diameter through A. Then the repulsionexerted on unit charge at P, by one of these strips atdistance d from P, of breadth das, and having D, F forits extremities, is equal to the repulsion of the incompletecircular strip of radius a?, breadth dx, and intercepted betweenthe lines PD
The London, Edinburgh and Dublin philosophical magazine and journal of science . ows. Imagine the circle AEB (fig. 1) replacedby a uniformly charged disk and calculate the repulsion ofthe disk on a unit charge placed at P. This will be mosteasily done by dividing the disk into narrow strips all atright angles to the diameter through A. Then the repulsionexerted on unit charge at P, by one of these strips atdistance d from P, of breadth das, and having D, F forits extremities, is equal to the repulsion of the incompletecircular strip of radius a?, breadth dx, and intercepted betweenthe lines PD and PF. 3. A distribution of electricity on a plane conductor boundedbij two close, similar, and similarly situated ellipses, anda uniform current in the confocal ellipse through the pointconsidered. To generalize the theorem of § 1 consider the spacebetween the ellipses of which the equations are 9 9 9 9 ~2 + 72—* o+j72=/C-d/C. . (3) ar tr or Ir One of these is shown by the heavy curve in fig. 3. Wetake an element of elliptic arc at E of length ds, and suppose FW. that over the area of this length, which lies at E betweenthe two curves, electricity is distributed with uniform sur-face density a. If the length of the perpendicular from the Electrostatic and Magnetic Fields. 475 centre on the tangent at E is p, the area is ^pdsd/t/x, and sothe charge is ^crpdsdK/K. Now through P let an ellipse confocal with the givenellipse LAK be described. A point A on the latter curvecorresponds to P on the confocal, and a point E on theconfocal corresponds to E on the given ellipse. Join E toP and A to E. These lines have the same length, r. Letp be the length of the perpendicular from the centre onthe tangent at E, and 0 denote the angle between the lineAE and that perpendicular. Let also p0, 0Q be the corre-sponding quantities for the point P and the line EP. [Careof course is to be taken that the lines are reckoned in thedirections indicated by the letters, and that the perpen-dic
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
