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title: "Three thin, concentric spherical conducting shells have radii \\(a\\), \\(b\\), and \\(c\\), where \\(a < b < c\\). Initially, the innermost shell (radius \\(a\\)) and outermost shell (radius \\(c\\)) are uncharged, while the middle shell (radius \\(b\\)) carries a net positive charge \\(Q\\). The innermost shell and outermost shell are then connected by a thin conducting wire that passes through a small insulated hole in the middle shell. Once electrostatic equilibrium is established, what is the net charge \\(q_a\\) on the innermost shell?"
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url: "https://nerd-notes.com/ubq/118302/"
date_modified: "2026-08-04T08:08:52+00:00"
---

# Three thin, concentric spherical conducting shells have radii \(a\), \(b\), and \(c\), where \(a < b < c\). Initially, the innermost shell (radius \(a\)) and outermost shell (radius \(c\)) are uncharged, while the middle shell (radius \(b\)) carries a net positive charge \(Q\). The innermost shell and outermost shell are then connected by a thin conducting wire that passes through a small insulated hole in the middle shell. Once electrostatic equilibrium is established, what is the net charge \(q_a\) on the innermost shell?

Three thin, concentric spherical conducting shells have radii \(a\), \(b\), and \(c\), where \(a < b < c\). Initially, the innermost shell (radius \(a\)) and outermost shell (radius \(c\)) are uncharged, while the middle shell (radius \(b\)) carries a net positive charge \(Q\). The innermost shell and outermost shell are then connected by a thin conducting wire that passes through a small insulated hole in the middle shell. Once electrostatic equilibrium is established, what is the net charge \(q_a\) on the innermost shell?

![A cross-sectional diagram showing three concentric circular shells centered at a single origin. The innermost circle has radius \(a\), the middle circle has radius \(b\), and the outermost circle has radius \(c\), with \(a < b < c\). The middle circle is rendered with a solid line and is labeled with a charge \(Q\). The innermost and outermost circles are rendered with solid lines. A thin curved line representing a wire connects a point on the innermost circle to a point on the outermost circle, passing through a tiny gap in the middle circle without touching it. Radial dashed line segments extend from the center to each circle, labeled \(a\), \(b\), and \(c\) respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830931-JuZqps.jpg)

- **A.** \( -Q \dfrac{a(c - b)}{c(b - a)} \)
- **B.** \( Q \dfrac{a(c - b)}{b(c - a)} \)
- **C.** \( -Q \dfrac{a(c - b)}{b(c - a)} \)
- **D.** \( -Q \dfrac{b(c - a)}{c(b - a)} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118302/*