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A very long conducting tube (hollow cylinder) has inner
Chapter 22, Problem 40P(choose chapter or problem)
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +?, where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?. (a) Calculate the electric field in terms of ? and the distance r from the axis of the tube for (i) r < a ; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of r. (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?
Questions & Answers
QUESTION:
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +?, where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?. (a) Calculate the electric field in terms of ? and the distance r from the axis of the tube for (i) r < a ; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of r. (b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?
ANSWER:Introduction We have to electric field due to a uniformly charged wire. Step 1 When , the Gaussian surface will contain the charge only due to the line in which passes through the axis of the cylinder. Hence the electric field will be