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title: "A thin, conducting spherical shell of radius \\(a\\) carries a net positive charge \\(+Q\\). It is concentric with a larger thin, conducting spherical shell of radius \\(b\\) (where \\(b > a\\)) that is connected to ground, setting its electric potential to zero. Which of the following correctly pairs the electric potential \\(V_a\\) at the surface of the inner shell with the net charge \\(Q_{\\text{outer}}\\rangle\\) induced on the outer shell?"
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url: "https://nerd-notes.com/ubq/118142/"
date_modified: "2026-08-04T08:05:29+00:00"
---

# A thin, conducting spherical shell of radius \(a\) carries a net positive charge \(+Q\). It is concentric with a larger thin, conducting spherical shell of radius \(b\) (where \(b > a\)) that is connected to ground, setting its electric potential to zero. Which of the following correctly pairs the electric potential \(V_a\) at the surface of the inner shell with the net charge \(Q_{\text{outer}}\rangle\) induced on the outer shell?

A thin, conducting spherical shell of radius \(a\) carries a net positive charge \(+Q\). It is concentric with a larger thin, conducting spherical shell of radius \(b\) (where \(b > a\)) that is connected to ground, setting its electric potential to zero. Which of the following correctly pairs the electric potential \(V_a\) at the surface of the inner shell with the net charge \(Q_{\text{outer}}\rangle\) induced on the outer shell?

![Cross-sectional view in the xy-plane of two thin concentric conducting circular shells centered at the origin. The inner circle of radius a is drawn with a thin line, labeled with a radial arrow pointing from the origin to the rim labeled a, and a text label +Q placed near the top edge inside the inner circle. The outer circle of radius b is concentric and larger, with a radial arrow pointing from the origin to its rim labeled b. On the right side of the outer shell, a straight connecting wire extends horizontally outward to a standard ground symbol consisting of three parallel horizontal lines of decreasing length. No other labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830729-1VjiCF.jpg)

- **A.** \(V_a = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{a}\) and \(Q_{\text{outer}} = 0\)
- **B.** \(V_a = \dfrac{1}{4\pi\varepsilon_0}\left(\dfrac{Q}{a} - \dfrac{Q}{b}\right)\) and \(Q_{\text{outer}} = 0\)
- **C.** \(V_a = \dfrac{1}{4\pi\varepsilon_0}\left(\dfrac{Q}{a} - \dfrac{Q}{b}\right)\) and \(Q_{\text{outer}} = -Q\)
- **D.** \(V_a = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{a}\) and \(Q_{\text{outer}} = -Q\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118142/*