By E. R. Dobbs (auth.)
Professor Dobbs presents a sublime and transparent account of the topic, prime the coed from electrostatics via to Maxwell's equations and electromagnetic waves, overlaying the entire fabric wanted by means of a scholar taking classes on electrical energy and magnetism and electromagnetic waves.
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B) Electric current is the flux of current density j-dS. M agnetostatics 48 vacuum, p = - Ne. dS dt We define a current density vector j as the positive charge flowing per unit area per second at a point and so dq =jdS dt whenj, and hence v, is normal to dS. Otherwise (Fig. dS dt where the scalar products vdS cos () and jdS cos () are similar to those found for the electric flux (Fig. 4). 1) for a stream of electrons, where q = - e. 2) Electric current is thus the flux of current density and has an SI unit of 1 ampere equal to 1 coulomb per second, while current density is in amperes per square metre.
Where Pn are Legendre functions. 26) and exercise 1) anQ 4>3 = r- 3(1 - 3 cos 2 0) is the long-range potential of a linear quadrupole (exercise 3). These solutions can also be applied to such problems as a conducting sphere (exercise 5) or a dielectric sphere (exercise 6) in a uniform electric field. In each case the electric potentials can be used to obtain the electric fields from the polar components of grad 4>: (grad 4»r =04> and (grad 4»6 =! 17) In cylindrical polar coordinates (r, 4>, z) shown in Fig.
6(a)) is more complex than that for a conductor since the field penetrates the dielectric. In this case two 'image' charges are suggested (Fig. 6(a)), q2 at the virtual image position as before and q3 outside the dielectric to represent the field inside. From Fig. 6(b), the potentials at P and Q are then cP __1_(q1 P - 4nso r 1 + q2) r2 40 Electric potential and fields - QI (0) Fig. 6 (a) Point charge q at distance a from plane dielectric D of relative permittivity Gr. (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.