---
title: "A thin, hollow spherical shell of radius \\(R\\) carries a total charge \\(+Q\\) distributed uniformly over its surface. Which of the following qualitative graph descriptions best represents the magnitude of the electric field \\(E\\) as a function of radial distance \\(r\\) from the center of the shell?"
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url: "https://nerd-notes.com/ubq/117902/"
date_modified: "2026-08-04T08:02:30+00:00"
---

# A thin, hollow spherical shell of radius \(R\) carries a total charge \(+Q\) distributed uniformly over its surface. Which of the following qualitative graph descriptions best represents the magnitude of the electric field \(E\) as a function of radial distance \(r\) from the center of the shell?

A thin, hollow spherical shell of radius \(R\) carries a total charge \(+Q\) distributed uniformly over its surface. Which of the following qualitative graph descriptions best represents the magnitude of the electric field \(E\) as a function of radial distance \(r\) from the center of the shell?

![A cross-sectional view of a thin spherical shell of radius R centered at the origin. Plus signs are evenly spaced along the boundary of the shell to represent uniform surface charge +Q. A horizontal radial axis labeled r starts from the center and extends outward to the right, passing through r = R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830550-8b08WY.jpg)

- **A.** \(E = 0\) for \(r < R\), jumps abruptly at \(r = R\) to a maximum value, and decays proportional to \(1/r^2\) for \(r > R\).
- **B.** \(E\) increases linearly from zero at \(r = 0\) to a maximum value at \(r = R\), and decays proportional to \(1/r^2\) for \(r > R\).
- **C.** \(E\) decays proportional to \(1/r^2\) for all \(r > 0\), behaving identically to a point charge located at the origin.
- **D.** \(E\) remains at a non-zero constant value for \(r < R\), then decays proportional to \(1/r^2\) for \(r > R\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117902/*