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title: "An uncharged, thick conducting spherical shell has an inner radius \\(a\\) and an outer radius \\(b\\). A point charge \\(+q\\) is placed inside the hollow cavity at an off-center position located a distance \\(r_0\\) (\\(0 < r_0 < a\\)) from the center of the sphere. Which of the following correctly describes the total induced charge on the inner cavity surface and the spatial distribution of charge on the outer surface of the shell once electrostatic equilibrium is established?"
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url: "https://nerd-notes.com/ubq/118284/"
date_modified: "2026-08-04T08:08:38+00:00"
---

# An uncharged, thick conducting spherical shell has an inner radius \(a\) and an outer radius \(b\). A point charge \(+q\) is placed inside the hollow cavity at an off-center position located a distance \(r_0\) (\(0 < r_0 < a\)) from the center of the sphere. Which of the following correctly describes the total induced charge on the inner cavity surface and the spatial distribution of charge on the outer surface of the shell once electrostatic equilibrium is established?

An uncharged, thick conducting spherical shell has an inner radius \(a\) and an outer radius \(b\). A point charge \(+q\) is placed inside the hollow cavity at an off-center position located a distance \(r_0\) (\(0 < r_0 < a\)) from the center of the sphere. Which of the following correctly describes the total induced charge on the inner cavity surface and the spatial distribution of charge on the outer surface of the shell once electrostatic equilibrium is established?

![A cross-sectional view of a thick conducting spherical shell with inner radius a and outer radius b. The center of the concentric circles representing the shell is marked with a small dot labeled O. Inside the cavity of radius a, a positive point charge labeled +q is positioned at a distance r_0 to the right of center O, off-center. The region between radius a and radius b is shaded gray to represent the conducting material. Radius a is indicated by a dashed line with a dimension arrow labeled a from center O to the inner surface. Radius b is indicated by a dimension arrow labeled b from center O to the outer surface. The displacement of +q from center O is labeled r_0 with a horizontal arrow. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830918-llh25K.jpg)

- **A.** Total charge on inner surface: \(-q \left(1 - \dfrac{r_0}{a}\right)\) Outer surface charge distribution: Non-uniform
- **B.** Total charge on inner surface: \(-q\) Outer surface charge distribution: Non-uniform
- **C.** Total charge on inner surface: \(-q\) Outer surface charge distribution: Uniform
- **D.** Total charge on inner surface: \(+q\) Outer surface charge distribution: Uniform

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118284/*