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# A very long conducting tube (hollow cylinder) has inner ISBN: 9780321675460 31

## Solution for problem 40P Chapter 22

University Physics | 13th Edition

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Problem 40P

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?

Step-by-Step Solution:

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 Step 2 If , then the gaussian surface will pass through the conductor. Now, we know that the electric field inside the conductor is always zero. Hence in this region, the electric field is zero. Step 3 If we have , then the total charge per unit length is Hence the charge density of the Gaussian surface drawn with will be . Hence the electric field outside the cylinder will be

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##### ISBN: 9780321675460

This full solution covers the following key subjects: tube, Charge, unit, length, surface. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. Since the solution to 40P from 22 chapter was answered, more than 251 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 40P from chapter: 22 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “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?” is broken down into a number of easy to follow steps, and 125 words.

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