---
title: "A spherical capacitor consists of a solid conducting sphere of radius \\(a\\) surrounded by a thin concentric conducting spherical shell of radius \\(b\\) (where \\(b > a\\)). The space between the inner sphere and outer shell is a vacuum. Which of the following correctly gives the capacitance \\(C\\) of this spherical capacitor, as well as the limiting capacitance \\(C_\\infty\\) as the outer radius \\(b\\) approaches infinity?"
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url: "https://nerd-notes.com/ubq/118282/"
date_modified: "2026-08-04T08:08:38+00:00"
---

# A spherical capacitor consists of a solid conducting sphere of radius \(a\) surrounded by a thin concentric conducting spherical shell of radius \(b\) (where \(b > a\)). The space between the inner sphere and outer shell is a vacuum. Which of the following correctly gives the capacitance \(C\) of this spherical capacitor, as well as the limiting capacitance \(C_\infty\) as the outer radius \(b\) approaches infinity?

A spherical capacitor consists of a solid conducting sphere of radius \(a\) surrounded by a thin concentric conducting spherical shell of radius \(b\) (where \(b > a\)). The space between the inner sphere and outer shell is a vacuum. Which of the following correctly gives the capacitance \(C\) of this spherical capacitor, as well as the limiting capacitance \(C_\infty\) as the outer radius \(b\) approaches infinity?

![A cross-sectional view of two concentric circles centered at the origin of a two-dimensional plane. The inner circle is solid gray with radius labeled \(a\), indicated by a black arrow extending from the central origin to the boundary of the inner circle with label \(a\) positioned beside the arrow. The outer circle is a thin black ring with radius labeled \(b\), indicated by a second black arrow extending from the central origin to the outer ring at a 45-degree angle above the horizontal, with label \(b\) near its arrowhead. The region between the inner circle and outer ring is white and unshaded. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830917-pNThPP.jpg)

- **A.** \(C = 4\pi\varepsilon_0 \dfrac{ab}{b-a}\) and \(C_\infty = 4\pi\varepsilon_0 a\)
- **B.** \(C = 4\pi\varepsilon_0 \dfrac{ab}{b-a}\) and \(C_\infty = \infty\)
- **C.** \(C = 4\pi\varepsilon_0 \dfrac{a^2}{b-a}\) and \(C_\infty = 0\)
- **D.** \(C = 4\pi\varepsilon_0 \dfrac{a^2}{b-a}\) and \(C_\infty = 4\pi\varepsilon_0 a\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118282/*