---
title: "Three concentric, thin, spherical conducting shells have radii \\(R\\), \\(2R\\), and \\(4R\\). Initially, the innermost shell has a net charge of \\(+Q\\), the middle shell has a net charge of \\(-6Q\\), and the outermost shell has a net charge of \\(+5Q\\). A thin conducting wire with an open switch connects the innermost shell to the outermost shell, passing through a small insulated hole in the middle shell without touching it. After the switch is closed and electrostatic equilibrium is established, what is the final net charge on the innermost shell?"
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url: "https://nerd-notes.com/ubq/124723/"
date_modified: "2026-09-28T14:09:27+00:00"
---

# Three concentric, thin, spherical conducting shells have radii \(R\), \(2R\), and \(4R\). Initially, the innermost shell has a net charge of \(+Q\), the middle shell has a net charge of \(-6Q\), and the outermost shell has a net charge of \(+5Q\). A thin conducting wire with an open switch connects the innermost shell to the outermost shell, passing through a small insulated hole in the middle shell without touching it. After the switch is closed and electrostatic equilibrium is established, what is the final net charge on the innermost shell?

Three concentric, thin, spherical conducting shells have radii \(R\), \(2R\), and \(4R\). Initially, the innermost shell has a net charge of \(+Q\), the middle shell has a net charge of \(-6Q\), and the outermost shell has a net charge of \(+5Q\). A thin conducting wire with an open switch connects the innermost shell to the outermost shell, passing through a small insulated hole in the middle shell without touching it. After the switch is closed and electrostatic equilibrium is established, what is the final net charge on the innermost shell?

![A cross-sectional schematic diagram showing three concentric circular boundaries centered at the origin, with radii labeled \(R\), \(2R\), and \(4R\). The innermost circular shell of radius \(R\) is labeled \(+Q\). The intermediate circular shell of radius \(2R\) is labeled \(-6Q\). The outermost circular shell of radius \(4R\) is labeled \(+5Q\). A single thin line representing a wire starts on the innermost shell, extends radially outward through a small gap in the intermediate shell without touching it, and terminates on the outermost shell. Along this radial wire line, between radius \(2R\) and radius \(4R\), there is an open single-pole switch symbol labeled S. Radial dashed lines with arrows from the center indicate the radii \(R\), \(2R\), and \(4R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604567-GhU34M.jpg)

- **A.** \(0\)
- **B.** \(+Q\)
- **C.** \(+2Q\)
- **D.** \(+3Q\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124723/*