**Problem Description:**A long coaxial cable carries a uniform **volume charge density** \( \rho \) on the inner cylinder (radius \( a \)) and a uniform **surface charge density** on the outer cylindrical shell (radius \( b \)). The surface charge is negative and of just the right magnitude so that the cable as a whole is electrically neutral.**Task:**Find the electric field, \( \mathbf{E}(s) \), in each of the three regions:1. **Inside the inner cylinder** (\( s < a \))2. **Between the cylinders** (\( a < s < b \))3. **Outside the cable** (\( s > b \))**Additionally:**Sketch \( \mathbf{E}(s) \) vs. \( s \).**Diagram Explanation:**The accompanying diagram illustrates a cross-section of the coaxial cable. It consists of:- An inner solid cylinder, shaded dark, with radius \( a \) representing the region of volume charge density \( \rho \).- An outer cylindrical shell surrounding the inner cylinder with a radius \( b \) indicating the surface charge density on its surface.The electric fields need to be calculated internally for different regions and plotted against the radial distance \( s \).

Answered: Image /qna-images/answer/655a2565-0ff6-47a2-a449-e7959aade76f.jpg

A long coaxial cable carries a uniform volume charge density p on the inner cylinder (radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). The surface charge is negative and of just the right magni- tude so that the cable as a whole is electrically neutral. Find the electric field, E(s), in each of the three regions: (i) inside the inner cylinder (s < a), (ii) between the cylinders (a < s < b), and (iii) outside the cable (s > b). Sketch E(s) vs. s.

A long coaxial cable carries a uniform volume charge density p on the inner cylinder (radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). The surface charge is negative and of just the right magni- tude so that the cable as a whole is electrically neutral. Find the electric field, E(s), in each of the three regions: (i) inside the inner cylinder (s < a), (ii) between the cylinders (a < s < b), and (iii) outside the cable (s > b). Sketch E(s) vs. s.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

**Problem Description:**

A long coaxial cable carries a uniform **volume charge density** \( \rho \) on the inner cylinder (radius \( a \)) and a uniform **surface charge density** on the outer cylindrical shell (radius \( b \)). The surface charge is negative and of just the right magnitude so that the cable as a whole is electrically neutral.

**Task:**

Find the electric field, \( \mathbf{E}(s) \), in each of the three regions:

1. **Inside the inner cylinder** (\( s < a \))
2. **Between the cylinders** (\( a < s < b \))
3. **Outside the cable** (\( s > b \))

**Additionally:**

Sketch \( \mathbf{E}(s) \) vs. \( s \).

**Diagram Explanation:**

The accompanying diagram illustrates a cross-section of the coaxial cable. It consists of:

- An inner solid cylinder, shaded dark, with radius \( a \) representing the region of volume charge density \( \rho \).
- An outer cylindrical shell surrounding the inner cylinder with a radius \( b \) indicating the surface charge density on its surface.

The electric fields need to be calculated internally for different regions and plotted against the radial distance \( s \).

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