---
title: "An infinitely long, nonconducting thick cylindrical shell has an inner radius \\(a\\) and an outer radius \\(b\\). The shell carries a uniform volume charge density \\(\\rho_0\\). Which of the following expressions gives the magnitude of the electric field at a radial distance \\(r\\) from the central axis within the shell wall, where \\(a < r < b\\), in terms of given quantities and fundamental constants?"
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url: "https://nerd-notes.com/ubq/117966/"
date_modified: "2026-08-04T08:02:43+00:00"
---

# An infinitely long, nonconducting thick cylindrical shell has an inner radius \(a\) and an outer radius \(b\). The shell carries a uniform volume charge density \(\rho_0\). Which of the following expressions gives the magnitude of the electric field at a radial distance \(r\) from the central axis within the shell wall, where \(a < r < b\), in terms of given quantities and fundamental constants?

An infinitely long, nonconducting thick cylindrical shell has an inner radius \(a\) and an outer radius \(b\). The shell carries a uniform volume charge density \(\rho_0\). Which of the following expressions gives the magnitude of the electric field at a radial distance \(r\) from the central axis within the shell wall, where \(a < r < b\), in terms of given quantities and fundamental constants?

![A three-dimensional perspective view of a long, thick cylindrical shell centered on a horizontal dashed axis labeled z. The inner cylinder surface has radius a and the outer cylinder surface has radius b. The volume between radius a and radius b is filled with light grey shading. A dashed coaxial cylinder of radius r and length L is positioned inside the shaded wall region, where a < r < b. An arrow labeled r extends radially outward from the central axis to the dashed cylinder. Arrows labeled a and b extend from the central axis to the inner and outer surfaces, respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830563-nmBuC8.jpg)

- **A.** \(\dfrac{\rho_0 r}{2\varepsilon_0}\)
- **B.** \(\dfrac{\rho_0 (r - a)}{2\varepsilon_0}\)
- **C.** \(\dfrac{\rho_0 (b^2 - a^2)}{2\varepsilon_0 r}\)
- **D.** \(\dfrac{\rho_0 (r^2 - a^2)}{2\varepsilon_0 r}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117966/*