---
title: "Two concentric, thin spherical conducting shells have radii \\(R\\) and \\(3R\\). The inner shell carries a net charge \\(+Q\\), and the outer shell carries a net charge \\(-2Q\\). The electric potential is defined to be zero at infinity (\\(V(\\infty) = 0\\)). Which of the following correctly describes the qualitative behavior of the electric potential \\(V(r)\\) as a function of radial distance \\(r\\) from the common center?"
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url: "https://nerd-notes.com/ubq/121068/"
date_modified: "2026-08-23T04:57:41+00:00"
---

# Two concentric, thin spherical conducting shells have radii \(R\) and \(3R\). The inner shell carries a net charge \(+Q\), and the outer shell carries a net charge \(-2Q\). The electric potential is defined to be zero at infinity (\(V(\infty) = 0\)). Which of the following correctly describes the qualitative behavior of the electric potential \(V(r)\) as a function of radial distance \(r\) from the common center?

Two concentric, thin spherical conducting shells have radii \(R\) and \(3R\). The inner shell carries a net charge \(+Q\), and the outer shell carries a net charge \(-2Q\). The electric potential is defined to be zero at infinity (\(V(\infty) = 0\)). Which of the following correctly describes the qualitative behavior of the electric potential \(V(r)\) as a function of radial distance \(r\) from the common center?

![A cross-sectional diagram showing two concentric circular boundaries centered at a common origin dot. The inner circle has a radius arrow labeled R and is marked with charge +Q. The outer concentric circle has a radius arrow labeled 3R and is marked with charge -2Q. A dashed radial axis extends from the origin through both shells to the right, labeled r. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461060-xzVKcq.jpg)

- **A.** Discontinuous with \(V = 0\) for \(0 \le r < R\), jumps to a positive maximum at \(r = R\), decreases monotonically toward zero for \(R < r < 3R\), and jumps discontinuously to a negative value at \(r = 3R\) before increasing toward zero as \(r \to \infty\).
- **B.** Constant and positive for \(0 \le r \le R\), decreases monotonically to zero at \(r = 3R\), and remains equal to zero for all \(r \ge 3R\).
- **C.** Constant and negative for \(0 \le r \le R\), decreases monotonically to a more negative value across \(R \le r \le 3R\), and increases toward zero from below for \(r \ge 3R\), remaining continuous everywhere.
- **D.** Constant and positive for \(0 \le r \le R\), decreases monotonically from positive to negative values for \(R \le r \le 3R\), and increases monotonically toward zero from below for \(r \ge 3R\), remaining continuous everywhere.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121068/*