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title: "A spherical capacitor consists of an inner solid conducting sphere of radius \\(a\\) carrying charge \\(+Q\\) and an outer concentric thin conducting spherical shell of radius \\(b\\) carrying charge \\(-Q\\). The space between the conductors is evacuated. Which of the following expressions gives the total electric energy stored in the electric field within the concentric region from \\(r’ = a\\) to \\(r’ = r\\), where \\(a < r < b\\)?"
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url: "https://nerd-notes.com/ubq/118268/"
date_modified: "2026-08-04T08:08:30+00:00"
---

# A spherical capacitor consists of an inner solid conducting sphere of radius \(a\) carrying charge \(+Q\) and an outer concentric thin conducting spherical shell of radius \(b\) carrying charge \(-Q\). The space between the conductors is evacuated. Which of the following expressions gives the total electric energy stored in the electric field within the concentric region from \(r’ = a\) to \(r’ = r\), where \(a < r < b\)?

A spherical capacitor consists of an inner solid conducting sphere of radius \(a\) carrying charge \(+Q\) and an outer concentric thin conducting spherical shell of radius \(b\) carrying charge \(-Q\). The space between the conductors is evacuated. Which of the following expressions gives the total electric energy stored in the electric field within the concentric region from \(r' = a\) to \(r' = r\), where \(a < r < b\)?

![A two-dimensional cross-sectional diagram of a spherical capacitor centered at the origin. An inner solid circle of radius a is filled with light gray shading and labeled +Q at its center. A concentric thin outer circle of radius b is drawn with a solid line and labeled -Q. A dashed concentric circle of radius r lies between the inner circle and outer shell, with a < r < b. The region between radius a and radius r is highlighted with light shading. Radial line segments extend from the center to indicate radii: one arrow labeled a pointing to the inner boundary, one arrow labeled r pointing to the dashed boundary, and one arrow labeled b pointing to the outer shell boundary. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830909-sWT0Ca.jpg)

- **A.** \(\dfrac{Q^2}{8\pi\varepsilon_0 r}\)
- **B.** \(\dfrac{Q^2}{16\pi\varepsilon_0} \left(\dfrac{1}{a} - \dfrac{1}{r}\right)\)
- **C.** \(\dfrac{Q^2}{8\pi\varepsilon_0} \left(\dfrac{1}{a^2} - \dfrac{1}{r^2}\right)\)
- **D.** \(\dfrac{Q^2}{8\pi\varepsilon_0} \left(\dfrac{1}{a} - \dfrac{1}{r}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118268/*