Page 66 - Engineering Electromagnetics, 8th Edition

3 CHAPTER

Electric Flux Density,

Gauss’s Law, and

Divergence

fter drawing a few of the fields described in the previous chapter and becom-
ing familiar with the concept of the streamlines that show the direction of
A the force on a test charge at every point, it is difficult to avoid giving these
lines a physical significance and thinking of them as flux lines. No physical particle
is projected radially outward from the point charge, and there are no steel tentacles
reaching out to attract or repel an unwary test charge, but as soon as the streamlines
are drawn on paper there seems to be a picture showing “something” is present.
It is very helpful to invent an electric flux that streams away symmetrically from a
point charge and is coincident with the streamlines and to visualize this flux wherever
an electric field is present.
This chapter introduces and uses the concept of electric flux and electric flux
density to again solve several of the problems presented in Chapter 2. The work here
turns out to be much easier, and this is due to the extremely symmetrical problems
that we are solving. ■

3.1 ELECTRIC FLUX DENSITY
About 1837, the director of the Royal Society in London, Michael Faraday, became
very interested in static electric fields and the effect of various insulating materials on
these fields. This problem had been bothering him during the past ten years when he
wasexperimenting in his now-famous work on induced electromotive force, which
we will discuss in Chapter 10. With that subject completed, he had a pair of concentric
metallicspheresconstructed,theouteroneconsistingoftwohemispheresthatcouldbe
firmly clamped together. He also prepared shells of insulating material (or dielectric
material, or simply dielectric) that would occupy the entire volume between the
concentric spheres. We will immediately use his findings about dielectric materials,
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