Use Gauss' Law to find the charge enclosed by the cube with vertices (±1,±1±1) if the electric field is E(x, y, z) = (x, y, z).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...
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1. Let E be an electric field and let the electric flux of E through
a surface S be given by the surface integral
Enux = [/ E d
S
One important law of electrostatics is Gauss' Law, which says
that the net charge enclosed by a closed surface S is given by
€0
E· dS,
where €o is a constant (called the permittivity of free space) that
depends on the units used in the problem.
1
Use Gauss' Law to find the charge enclosed by the cube with
vertices (±1, ±l±1) if the electric field is E(x, Y, z) = (x, y, z).
Note: Your final answer will contain the constant e0.
Transcribed Image Text:1. Let E be an electric field and let the electric flux of E through a surface S be given by the surface integral Enux = [/ E d S One important law of electrostatics is Gauss' Law, which says that the net charge enclosed by a closed surface S is given by €0 E· dS, where €o is a constant (called the permittivity of free space) that depends on the units used in the problem. 1 Use Gauss' Law to find the charge enclosed by the cube with vertices (±1, ±l±1) if the electric field is E(x, Y, z) = (x, y, z). Note: Your final answer will contain the constant e0.
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