Problem 23.27Figure 7 is a section of a conducting rod of radiusR1= 1.3mmand lengthL= 11minside ofa thin-walled coaxial conducting cylindrical shell of radiusR2= 10R1and the same lengthL.The net charge on the rod isQ1= +3.4×10-12C; that on the shell isQ2=-2Q1. What arethea)magnitudeEandb)direction of the electric field at radial distancer= 2R2? What arec)Eandd)the direction atr= 5R1? What is the charge on thee)interior andf)exteriorsurface of the shell?Figure 7: Two coaxial cylindrical conductors.Parts a) and b)Because of the cylindrical symmetry of the problem, we can see immediatelythat the most useful Gaussian surface will be the cylinder. Notice that the problem states that thisis a section from a much longer rod and hence we can treat this as an infinite rod. This allows usto exploit the cylindrical symmetry of the problem and say that the field from both pieces must bedirected radially and must be constant at equal radial distances from the center of the conductor.
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