Adapted from 22.37 in your book: A long coaxial cable consists of an inner cylin

Question

Adapted from 22.37 in your book: A long coaxial cable consists of an inner cylindrical conductor with radius 1.00 mm and an outer coaxial conducting cylinder with inner radius 4.0 mm and outer radius 5.0 mm. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform charge per unit length of 1.0 C/m. a) Calculate the electric field in the space between the cylinders. b) Calculate the electric field outside the outer cylinder. c) What is the electric field in the interior of the outer cylinder? d) Find the charge per unit length on the inner surface and the outer surface of the cylinder.

Explanation / Answer

= Q / 0 = EA        Gauss' Law E = (Q / L) / (2 R 0)      since the area ofa cylindrical Gaussian surface is 2 R L E = 1 / (2 R 0) = 1.80 * 10E10 /R  N/C          .001< R < .004 m     in the spacebetween the cylinders b) E = 1.80 * 10E10 / R  N/C        .005 < R<         thefield outside the outer cylinder      The charge on the inner cylinder willinduce an equal & opposite charge on the inner surface of theouter cylinder.       This will leave a net charge onthe outer surface of the outer cylinder equal to that on theinner cylinder. Since the magnitude of the charge on the surfaces of thecylinders is the same the charge per unit length must be the same on all threesurfaces. c) The field within the outer cylinder must be zero otherwisea current would flow within the conductor.      Also, an imaginary cylindricalGaussian surface within the outer cylinder would contain no netcharge.

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