---
title: "A solid conducting sphere of radius \\(a\\) carrying a net charge \\(+Q\\) is concentric with an uncharged, thin spherical conducting shell of radius \\(b\\), where \\(b > a\\). A thin conducting wire containing an open switch connects the inner sphere to the outer shell. The switch is now closed, and the system is allowed to reach electrostatic equilibrium. Assuming the electric potential is zero at infinity (\\(V(\\infty) = 0\\)), which of the following best describes the shape of the electric potential \\(V(r)\\) as a function of radial distance \\(r\\) from the center?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/121131/"
date_modified: "2026-08-23T04:58:14+00:00"
---

# A solid conducting sphere of radius \(a\) carrying a net charge \(+Q\) is concentric with an uncharged, thin spherical conducting shell of radius \(b\), where \(b > a\). A thin conducting wire containing an open switch connects the inner sphere to the outer shell. The switch is now closed, and the system is allowed to reach electrostatic equilibrium. Assuming the electric potential is zero at infinity (\(V(\infty) = 0\)), which of the following best describes the shape of the electric potential \(V(r)\) as a function of radial distance \(r\) from the center?

A solid conducting sphere of radius \(a\) carrying a net charge \(+Q\) is concentric with an uncharged, thin spherical conducting shell of radius \(b\), where \(b > a\). A thin conducting wire containing an open switch connects the inner sphere to the outer shell. The switch is now closed, and the system is allowed to reach electrostatic equilibrium. Assuming the electric potential is zero at infinity (\(V(\infty) = 0\)), which of the following best describes the shape of the electric potential \(V(r)\) as a function of radial distance \(r\) from the center?

![A cross-sectional diagram showing a central solid circle of radius a and a concentric thin circular ring of radius b. A dashed radial segment connects the outer boundary of the inner circle to the inner edge of the circular ring, interrupted by an open switch symbol labeled S. A centered label +Q is located inside the inner circle. The radius of the inner circle is indicated by a solid arrow from the center to its edge labeled a, and the radius of the outer ring is indicated by a solid arrow from the center to its edge labeled b. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461094-irdYHp.jpg)

- **A.** It is constant and positive for \(0 \le r \le a\), decreases proportional to \(\dfrac{1}{r}\) for \(a < r < b\), and continues decreasing proportional to \(\dfrac{1}{r}\) for \(r \ge b\).
- **B.** It is zero for \(0 \le r \le b\), and decreases proportional to \(\dfrac{1}{r}\) toward zero for \(r > b\).
- **C.** It is constant and positive for \(0 \le r \le b\), and decreases smoothly proportional to \(\dfrac{1}{r}\) toward zero for \(r > b\).
- **D.** It is constant and positive for \(0 \le r \le a\), drops discontinuously to a lower positive constant value for \(a < r \le b\), and decreases proportional to \(\dfrac{1}{r}\) for \(r > b\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121131/*