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The Coaxial Cable. A long coaxial cable consists of an
Chapter 22, Problem 39P(choose chapter or problem)
The Coaxial Cable. A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length ?. Calculate the electric field (a) at any point between the cylinders a distance r from the axis and (b) at any point outside the outer cylinder. (c) Graph the magnitude of the electric field as a function of the distance r from the axis of the cable, from r = 0 to r = 2c. (d) Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.
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QUESTION:
The Coaxial Cable. A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length ?. Calculate the electric field (a) at any point between the cylinders a distance r from the axis and (b) at any point outside the outer cylinder. (c) Graph the magnitude of the electric field as a function of the distance r from the axis of the cable, from r = 0 to r = 2c. (d) Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.
ANSWER:Introduction We have to calculate the electric field any point in between the cylinders and outside the cylinder. Step 1 Let us now consider a cylindrical Gaussian surface of radiand length from whose axis is matching with the axis of the coaxial cable. Now only the electric field will pass only through the curved surface and hence the flux through the Gaussian surface is And from the Gauss’s law, we can write that the flux through the gaussian surface is given by Here is the linear charge density. So we have