By E. R. Dobbs (auth.)
Professor Dobbs offers a sublime and transparent account of the topic, best the coed from electrostatics via to Maxwell's equations and electromagnetic waves, protecting the entire fabric wanted via a scholar taking classes on electrical energy and magnetism and electromagnetic waves.
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Formally, (A (A 0 ~ 0 ~ 0 ) . o) The scalar and vector fields resulting from the operations of \7 2 , grad, div and curl are here expressed in Cartesian coordinates, but their importance in vector analysis arises from their independence of any particular coordinate system. The latter can then be chosen according to the symmetry of the problem to which the differential equations are being applied. 14) This is Poisson's equation for the electrostatic potential 4> in the presence of an electric charge density p.
Unlike photons, electrons repel one another and so an incident parallel beam slowly diverges producing an electronic aberration. An example of an astigmatic electron lens is a combination of two quadrupole lenses with alternate potentials, the first producing a Fig. 12 Field lines (--) and hyperbolic conductors (+ V, - V) for a cross-section of an electric quadrupole lens. 46 Electric potential and fields diverging focus and the second a converging focus. If the lenses have focal lengths fl = - f2 = f and are separated by a distance d, the combination has a focal length f2/d, by analogy with a pair of thin optical lenses.
B) The image charge q2 at distance 2a from ql for fields outside the dielectric and the image charge q3 for fields inside the dielectric replace the dielectric material. 25) However, since 4>p = 4>Q for all values of 8, m = 1. Therefore q3 coincides with ql and is the image of q2 in the surface. 33), is DPn = D Qn or o4>p o4>Q -=e - - ax r ax since there is no free charge density at the surface of a dielectric. 26) Electron optics 41 o Fig. 7 Electric displacement lines ( -+- ) from the charge q near the plane dielectric D of relative permittivity Gr' Sections through one equipotential surface in the dielectric and four outside it are shown (......
Basic Electromagnetism by E. R. Dobbs (auth.)