---
title: "A long, nonconducting solid cylinder of radius \\(R\\) carries a uniform volume charge density \\(\\rho\\). The electric potential at the surface of the cylinder is set to zero, so \\(V(R) = 0\\). Which of the following expressions gives the electric potential \\(V(r)\\) inside the cylinder (\\(r < R\\)) as a function of distance \\(r\\) from the central axis?"
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url: "https://nerd-notes.com/ubq/118092/"
date_modified: "2026-08-04T08:05:04+00:00"
---

# A long, nonconducting solid cylinder of radius \(R\) carries a uniform volume charge density \(\rho\). The electric potential at the surface of the cylinder is set to zero, so \(V(R) = 0\). Which of the following expressions gives the electric potential \(V(r)\) inside the cylinder (\(r < R\)) as a function of distance \(r\) from the central axis?

A long, nonconducting solid cylinder of radius \(R\) carries a uniform volume charge density \(\rho\). The electric potential at the surface of the cylinder is set to zero, so \(V(R) = 0\). Which of the following expressions gives the electric potential \(V(r)\) inside the cylinder (\(r < R\)) as a function of distance \(r\) from the central axis?

![A circular cross section of a solid cylinder of radius R centered at the origin. The circle of radius R is filled with uniform light gray shading. A smaller concentric dashed circle of radius r (where r < R) represents an internal cylindrical Gaussian surface. An arrow labeled r extends from the central axis to the dashed circle, and an arrow labeled R extends from the central axis to the outer boundary. No other labels or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/cylinder-cross-section-1785830703-ktESYe.jpg)

- **A.** \(\dfrac{\rho}{2\varepsilon_0} (R^2 - r^2)\)
- **B.** \(\dfrac{\rho}{4\varepsilon_0} (R^2 - r^2)\)
- **C.** \(\dfrac{\rho}{4\varepsilon_0} \left(R^2 - \dfrac{r^3}{R}\right)\)
- **D.** \(\dfrac{\rho}{2\varepsilon_0} r(R - r)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118092/*