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We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: Genc= On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E= Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc- On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in simplified form is E =

We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: Genc= On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E= Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc- On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in simplified form is E =

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter25: Gauss’s Law
Section: Chapter Questions
Problem 68PQ: Examine the summary on page 780. Why are conductors and charged sources with linear symmetry,...
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An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire)

 

 

We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: Genc = On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E = Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc= On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in simplified form is E =
Transcribed Image Text:We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: Genc = On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E = Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc= On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in simplified form is E =
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