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CourseNotes.11 - Problem 23.27 Figure 7 is a section of a...

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Problem 23.27 Figure 7 is a section of a conducting rod of radius R 1 = 1 . 3 mm and length L = 11 m inside of a thin-walled coaxial conducting cylindrical shell of radius R 2 = 10 R 1 and the same length L . The net charge on the rod is Q 1 = +3 . 4 × 10 - 12 C ; that on the shell is Q 2 = - 2 Q 1 . What are the a) magnitude E and b) direction of the electric field at radial distance r = 2 R 2 ? What are c) E and d) the direction at r = 5 R 1 ? What is the charge on the e) interior and f) exterior surface of the shell? Figure 7: Two coaxial cylindrical conductors. Parts a) and b) Because of the cylindrical symmetry of the problem, we can see immediately that the most useful Gaussian surface will be the cylinder. Notice that the problem states that this is a section from a much longer rod and hence we can treat this as an infinite rod. This allows us to exploit the cylindrical symmetry of the problem and say that the field from both pieces must be directed radially and must be constant at equal radial distances from the center of the conductor.
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