Basic Electromagnetism by E. R. Dobbs (auth.)

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By E. R. Dobbs (auth.)

Professor Dobbs presents a sublime and transparent account of the topic, major the scholar from electrostatics via to Maxwell's equations and electromagnetic waves, masking all of the fabric wanted through a pupil taking classes on electrical energy and magnetism and electromagnetic waves.

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V, Fig. 8 Electrons at velocity Vl in the equipotential region V1 are refracted from an incident angle (}l to an emergent angle (}2 at velocity V 2 in the equipotential region V2 • Electron optics I:t l I I I 43 :• \ ~ \\, : I , \ I ~ \ \ \ : I ~ II:III li//r:'/ I I I I' o :: I v : : I I I (0 ) Fig. 9 Electric field lines (-+-) and equipotentials (----) for (a) a single pair, and (b) a double pair of apertures. / > / I V2 (b) Fig. 10 Electric field lines (-+-) and equipotentials (----) for (a) an accelerating, and (b) a decelerating cylindrical lens.

Referring to Fig. 12 we can see that this amount of work would also be done if the charge was just moved radially from a' to b. Equally it would be the same if it was moved first along the radial path aa", then along the circular path a" b' and finally along the radial path b' b, since E is always normal to a circular path about q and therefore no work is done along a circular path. E'ds is the same along any arbitrary path which can always be considered as the zero sum of normal components along circular paths and the work done by the tangential components along radial paths.

1 Thin electrostatic lens In practice a lens of the type shown in Fig. 9(b) would have thick electrodes with rounded corners to avoid edge effects, as shown in Fig. 11(a). 18), becomes ~~(rofjJ)+ o2fjJ =0 r or Integrating or OZ2 Electric potential and fields 44 ~---~-1i---p R : ... , ... : ........... 1 ~ -+----------~o--~~--~~---z : :... ll (a) Paraxial electron path through an aperture showing the focal length of the lens. (b) Axial and radial electron moments, pz and Pro Thus or 2 OZ2 For electrons following paraxial trajectories, the axial velocity is dz/dt at any point, while the radial momentum due to the radial force eo

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