By E. R. Dobbs (auth.)
Professor Dobbs offers a chic and transparent account of the topic, prime the scholar from electrostatics via to Maxwell's equations and electromagnetic waves, protecting all of the fabric wanted through a pupil taking classes on electrical energy and magnetism and electromagnetic waves.
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27) 25 Dielectrics The capacitance of the capacitor is inversely proportional to the potential and so to the electric field. 28) d Measurement of the electric susceptibility x. of matter at low frequencies is thus a measurement of the relative permittivity, en which at optical frequencies can be shown to be the square of the refractive index, as explained in Chapter 10. 9), Gauss's law: f E·dS=~ f s eo v pdr where V is the volume enclosed by the surface S. When dielectrics are present, the charge density p will be the sum of any polarization charges of density Pp and any free charges of density Pc.
38 Electric potential and fields that due to + q and the earthed conductor, by the uniqueness theorem. 13), where, from Fig. 23) The electric field lines are plotted in Fig. 5, together with two sections of equipotential surfaces, which cut the field lines normally everywhere. 24) At the surface r 1 = r2 and Eo points into the conductor, as the Fig. 5 Electric field lines ( ---+) from the charge q near the conducting plane C. Sections through two equipotential surfaces are shown as dotted lines ( ......
By the uniqueness theorem the electric potentials for a point charge plus its image are identical with those for a point charge and the conductor for the region outside the surface, since in both cases Laplace's equation is satisfied for all points outside the conductor. The method is illustrated by some examples here and exercises 8-10. 1 Point charge and plane conductor A simple example is a point charge + q near an earthed, infinite conducting plane (Fig. 4(a)). 21) as we showed from Fig. 13.