By William R. Smythe
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Additional resources for Static and Dynamic Electricity (with Solutions Manual)
If the force law were r-(2+P), prove that there would be a charge B on the inner shell such that if A were the charge on the outer shell and f, g the sum and difference of the radii 2gB = -Ap[(f - g) In (f + g) - f In f + g In g], approximately. 15C. Three infinite parallel wires cut a plane perpendicular to them in the angular points A, B, C of an equilateral triangle and have charges q, q, -q' per unit length, respectively. Prove that the extreme lines of force which pass from A to C make at starting angles (2q - 5q')7(6q)-' and - (2q q')7(6q)-1with AC, provided that q' > 2q.
In terms of the potential these boundary conditions may be written ,av' an E „av an " K' a' v or n Knav" an (5) V' = V" (6) where V' and V" are the potentials in e' and e". Equation (6) implies that the zero of potential is chosen in both mediums, so that at some point on the boundary V' = V". It then follows, by integration of (3), that (6) holds for all points on the boundary. The normal stresses directed from e" to e' on the interface between two dielectrics may also be written, from (2) and (4), F = T.
14) that all electrical stresses in a medium in an electric field depend on the intensity in the same way is that the equilibrium is undisturbed if the intensity everywhere in the field is changed by the same factor. 02 configuration of the field is unchanged but the intensity is doubled, and hence the work required to take a small charge from one conductor to another is also doubled. This constant charge to potential ratio of an isolated conductor is its capacitance, and the reciprocal ratio is its -21astance.
Static and Dynamic Electricity (with Solutions Manual) by William R. Smythe