Elements of the Mathematical Theory of Electricity And Magnetism
Elements of the Mathematical Theory of Electricity And Magnetism
J J Joseph John Thomson
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If the body at P is a small sphere of radius b, then since the elec- tric energy is equal to JS^F, it is in this case 1 (e ea 1 2 e \b~JPQ a or - n* 87, To find the surface density at a point S on the surface of the sphere, we must find the electric intensity along the normal. 88] ELECTRICAL IMAGES AND INVERSION 113 The electric intensity at S due to the charge e at P can by the triangle of forces be resolved into the two components e OS . () pa pg alon g ^ (ft) ~~ parallel to PO, while the ele...ctric intensity at S due to the charge ea/f at Q can be resolved into the components ea 1 OS (S) -^ parallel to PO. Hence the components of the resultant intensity are a + y along the normal OS, and j8 + 8 parallel to PO. Now the resultant intensity is along the normal, so that the component /? + 8 must vanish, and the resultant intensity along the normal is equal to a -h y, i. E. To JL _ a JLI PS 3 fQS*] e. OS e. OS or to ~~PQ3~ Since PS/QS is constant, the quantity inside the brackets is constant.
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