Concept explainers
Gauss’ Law for electric fields The electric field due to a point charge Q is
a. Show that the flux of the field across a sphere of radius a centered at the origin is
b. Let S be the boundary of the region between two spheres centered at the origin of radius a and b with a < b. Use the Divergence Theorem to show that the net outward flux across S is zero.
c. Suppose there is a distribution of charge within a region D Let q(x, y, z) be the charge density (charge per unit volume). Interpret the statement that
d. Assuming E satisfies the conditions of the Divergence Theorem on D. conclude from part (c) that
e. Because the electric force is conservative, it has a potential function ϕ. From part (d). conclude that
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Calculus: Early Transcendentals (2nd Edition)
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage