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title: "Three thin, concentric conducting spherical shells have radii \\(R\\), \\(2R\\), and \\(3R\\). The innermost shell carries a net charge of \\(+Q\\), the middle shell carries a net charge of \\(-2Q\\), and the outermost shell carries a net charge of \\(+Q\\). Which of the following best describes the magnitude of the electric field \\(E(r)\\) as a function of radial distance \\(r\\) from the common center of the shells?"
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url: "https://nerd-notes.com/ubq/118261/"
date_modified: "2026-08-04T08:08:28+00:00"
---

# Three thin, concentric conducting spherical shells have radii \(R\), \(2R\), and \(3R\). The innermost shell carries a net charge of \(+Q\), the middle shell carries a net charge of \(-2Q\), and the outermost shell carries a net charge of \(+Q\). Which of the following best describes the magnitude of the electric field \(E(r)\) as a function of radial distance \(r\) from the common center of the shells?

Three thin, concentric conducting spherical shells have radii \(R\), \(2R\), and \(3R\). The innermost shell carries a net charge of \(+Q\), the middle shell carries a net charge of \(-2Q\), and the outermost shell carries a net charge of \(+Q\). Which of the following best describes the magnitude of the electric field \(E(r)\) as a function of radial distance \(r\) from the common center of the shells?

![Three thin concentric nested circles are centered at an origin dot labeled O. A dashed horizontal line extends from the origin O to the right through all three circles. The innermost circle has radius R, indicated by a dimension line from the origin to its boundary labeled R, and carries a label +Q above its top edge. The middle circle has radius 2R, indicated by a dimension line from the origin to its boundary labeled 2R, and carries a label -2Q above its top edge. The outermost circle has radius 3R, indicated by a dimension line from the origin to its boundary labeled 3R, and carries a label +Q above its top edge. No other labels, vectors, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830908-dd6Lbp.jpg)

- **A.** \(E = 0\) for \(r < R\); jumps to \(E_0 = \dfrac{Q}{4\pi\varepsilon_0 R^2}\) at \(r = R\) and decays proportional to \(\dfrac{1}{r^2}\) to \(\dfrac{E_0}{4}\) at \(r = 2R\); stays at \(0\) for \(2R < r < 3R\); and remains \(0\) for \(r > 3R\).
- **B.** \(E = 0\) for \(r < R\); jumps to \(E_0 = \dfrac{Q}{4\pi\varepsilon_0 R^2}\) at \(r = R\) and decays proportional to \(\dfrac{1}{r^2}\) to \(\dfrac{E_0}{4}\) at \(r = 2R\); jumps at \(r = 2R\) to \(\dfrac{E_0}{2}\) and decays proportional to \(\dfrac{1}{r^2}\) to \(\dfrac{2E_0}{9}\) at \(r = 3R\); then drops to \(0\) for \(r > 3R\).
- **C.** \(E = 0\) for \(r < R\); jumps to \(E_0 = \dfrac{Q}{4\pi\varepsilon_0 R^2}\) at \(r = R\) and decays continuously proportional to \(\dfrac{1}{r^2}\) across the range \(R < r < 3R\), reaching \(\dfrac{E_0}{9}\) at \(r = 3R\); then drops abruptly to \(0\) for \(r > 3R\).
- **D.** \(E = 0\) for \(r < R\); jumps to \(E_0 = \dfrac{Q}{4\pi\varepsilon_0 R^2}\) at \(r = R\) and decays proportional to \(\dfrac{1}{r^2}\) to \(\dfrac{E_0}{4}\) at \(r = 2R\); drops to \(0\) at \(r = 2R\); jumps to \(E_0 = \dfrac{Q}{4\pi\varepsilon_0 R^2}\) at \(r = 3R\) and decays proportional to \(\dfrac{1}{r^2}\) for \(r > 3R\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118261/*