---
title: "Two concentric, thin spherical conducting shells have radii \\(R\\) and \\(3R\\). The inner shell carries a net charge \\(+Q\\), and the outer shell is initially uncharged. A switch connecting the outer shell to earth ground is then closed, bringing the outer shell to zero electric potential relative to infinity. Once electrostatic equilibrium is established, what is the electric potential at the surface of the inner shell relative to infinity?"
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url: "https://nerd-notes.com/ubq/121148/"
date_modified: "2026-08-23T04:58:18+00:00"
---

# Two concentric, thin spherical conducting shells have radii \(R\) and \(3R\). The inner shell carries a net charge \(+Q\), and the outer shell is initially uncharged. A switch connecting the outer shell to earth ground is then closed, bringing the outer shell to zero electric potential relative to infinity. Once electrostatic equilibrium is established, what is the electric potential at the surface of the inner shell relative to infinity?

Two concentric, thin spherical conducting shells have radii \(R\) and \(3R\). The inner shell carries a net charge \(+Q\), and the outer shell is initially uncharged. A switch connecting the outer shell to earth ground is then closed, bringing the outer shell to zero electric potential relative to infinity. Once electrostatic equilibrium is established, what is the electric potential at the surface of the inner shell relative to infinity?

![A cross-sectional diagram showing two concentric circular conducting shells centered on the same point. The inner shell is drawn as a thin circle with radius labeled R using an arrow from the center pointing up and to the left at 45 degrees. The region inside the inner shell contains a label +Q near the top. The outer shell is drawn as a concentric larger thin circle with radius labeled 3R using an arrow from the center pointing up and to the right at 45 degrees. At the rightmost edge of the outer shell, a wire extends horizontally to the right, connects to an open single-pole single-throw switch labeled S, and then leads to a standard ground symbol consisting of three horizontal parallel lines of decreasing width. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/concentric-shells-grounded-1787461098-IolD5C.jpg)

- **A.** \(0\)
- **B.** \(\dfrac{Q}{12\pi\varepsilon_0 R}\)
- **C.** \(\dfrac{Q}{6\pi\varepsilon_0 R}\)
- **D.** \(\dfrac{Q}{4\pi\varepsilon_0 R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121148/*