---
title: "An uncharged, solid conducting sphere of radius \\(R\\) contains an off-center spherical cavity of radius \\(r_0\\). A point charge \\(+q\\) is fixed inside the cavity at a location that is not at the center of the cavity. The system is in electrostatic equilibrium. Which of the following correctly pairs the potential difference \\(\\Delta V\\) between any two points on the outer surface of the sphere with the symmetry of the electric field \\(\\vec{E}\\) in the region outside the sphere (\\(r > R\\))?"
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url: "https://nerd-notes.com/ubq/118105/"
date_modified: "2026-08-04T08:05:09+00:00"
---

# An uncharged, solid conducting sphere of radius \(R\) contains an off-center spherical cavity of radius \(r_0\). A point charge \(+q\) is fixed inside the cavity at a location that is not at the center of the cavity. The system is in electrostatic equilibrium. Which of the following correctly pairs the potential difference \(\Delta V\) between any two points on the outer surface of the sphere with the symmetry of the electric field \(\vec{E}\) in the region outside the sphere (\(r > R\))?

An uncharged, solid conducting sphere of radius \(R\) contains an off-center spherical cavity of radius \(r_0\). A point charge \(+q\) is fixed inside the cavity at a location that is not at the center of the cavity. The system is in electrostatic equilibrium. Which of the following correctly pairs the potential difference \(\Delta V\) between any two points on the outer surface of the sphere with the symmetry of the electric field \(\vec{E}\) in the region outside the sphere (\(r > R\))?

![A 2D cross-section diagram of a large circle of radius R representing a solid conductor. Inside the large circle, offset to the upper-right of the center, is a smaller circle of radius r_0 representing a spherical cavity. A point labeled +q is shown inside the cavity, offset from the center of the cavity. The region between the small circle and large circle is shaded gray to indicate conducting material. The center of the large circle is marked with a point labeled O. A dashed line indicates the outer surface of radius R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830709-I4Q1Yq.jpg)

- **A.** \(\Delta V\) between outer surface points: Nonzero; Electric field for \(r > R\): Asymmetric, shifted toward the cavity side
- **B.** \(\Delta V\) between outer surface points: Zero; Electric field for \(r > R\): Spherically symmetric about the center of the outer sphere
- **C.** \(\Delta V\) between outer surface points: Zero; Electric field for \(r > R\): Asymmetric, shifted toward the cavity side
- **D.** \(\Delta V\) between outer surface points: Nonzero; Electric field for \(r > R\): Spherically symmetric about the center of the outer sphere

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118105/*