A long coaxial cable consists of an inner cylindrical conductor with radius a an
ID: 1524565 • Letter: A
Question
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 .
Part A
Calculate the magnitude of the electric field at any point between the cylinders a distance r from the axis.
Express your answer in terms of the variables a, b, c, r, and constants and 0.
E(r) = ___
Part C
Calculate the magnitude of the electric field at any point outside the outer cylinder a distance r from the axis.
Express your answer in terms of the variables a, b, c, r, and constants and 0.
E(r) = ___
Part E
Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.
Enter your answers in ascending order separated by a comma. Express them in terms of the given quantities.
inner,outer = ___
Explanation / Answer
a) first we have to find the electric field at any point between the cylinders a distance r from the axis.
imagine a gaussian surface as a cylinder of radius r and length l here a< r<b . Then by Gauss's law
E . ds =Q/0
ie , E . 2rl = l /0
E = l / 2rl 0 = / 2r 0 , for b> r > a
b) in the second part we have to find the field outside the outer cylinder.
here imagine a Gaussian surface of radius r and length l outside the outer cylinder. ie , r is greater than c
E . 2rl = l /0
E = l / 2rl 0 = / 2r 0 , for r>c
c) since the surface of inner conductor has linear charge density + , the surfaces of outer conductor must carry induced charges. it will have charge density - on its inner surface and + on its outer surface so that the net charge is zero as mentioned in the question.
inner = - , outer = +
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