4.3.1. Electrostatic force between loaded conductive spheres
Let us suppose that we have x denoting an electric field function produced by a loaded conductive sphere, with center in P = (0,0,0) point, plus an electron of the infinitesimal surface ds of another loaded conductive sphere placed in a Q = (x, 0, 0) point. This electron will be subject to an electric force F, given by 4.14, which according to Figure 9 will be:
Figure 9: Comments in the text
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The inductive effects were despised in a similar way to the dodge adopted in the analytic study of Coloumb’s law. This implies considering the electrons as fixed and restricted to a centrifugal direction. The force on ds will be, then:
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The dFy and dFz components are canceled in pairs. Therefore,
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With the aid of figure 9 we get to the following relationships:
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Substituting 4.18 in 4.16 and observing the value of x given by 4.11 for r > R, we obtain:
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The expression 4.19 is nothing but Coulomb's law, expressed in terms of the numbers of electrons N and N' contained in the considered Q and Q' charges.
