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By Jerrold Franklin

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The electric field is assumed to be finite throughout the region of the surface. Hence, as the area of the sideface shrinks to zero, so also does the contribution of the sideface to the surface integral. Thus, the displacement flux through the closed surface consists only of the contributions from the top and bottom surfaces. Applied to the pillbox, Gauss’ integral law requires that n · (�o Ea − �o Eb ) = σs (17) where the area A has been canceled from both sides of the equation. The contribution from the endface on side (b) comes with a minus sign because on that surface, n is opposite in direction to the surface element da.

2, confidence also comes from having these natural constants memorized. A common unit for measuring the magnetic flux density is the Gauss, so the conversion to the SI unit of Tesla is also given with the abbreviations. A goal in this chapter has also been the use of examples to establish the mathematical significance of volume, surface, and contour integrations. At the same time, important singular source distributions have been defined and their associated fields derived. We will make extensive use of point, line, and surface sources and the associated fields.

4 In a spherically symmetric configuration, the region r < b has the uniform charge density ρb and is surrounded by a region b < r < a having the uniform charge density ρa . At r = b there is no surface charge density, while at r = a there is that surface charge density that assures E = 0 for a < r. (a) Determine E in the two regions. (b) What is the surface charge density at r = a? (c) Now suppose that there is a surface charge density given at r = b of σs = σo . Determine E in the two regions and σs at r = a.

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