---
title: "A spherical capacitor consists of two concentric, thin conducting spherical shells of radii \\(a\\) and \\(b\\) (where \\(a < b\\)). The inner shell carries a net charge \\(+Q\\) and the outer shell carries a net charge \\(-Q\\). Which of the following best describes the graph of the electric energy density \\(u_E\\) stored in the electric field as a function of radial distance \\(r\\) from the common center?"
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url: "https://nerd-notes.com/ubq/118235/"
date_modified: "2026-08-04T08:08:20+00:00"
---

# A spherical capacitor consists of two concentric, thin conducting spherical shells of radii \(a\) and \(b\) (where \(a < b\)). The inner shell carries a net charge \(+Q\) and the outer shell carries a net charge \(-Q\). Which of the following best describes the graph of the electric energy density \(u_E\) stored in the electric field as a function of radial distance \(r\) from the common center?

A spherical capacitor consists of two concentric, thin conducting spherical shells of radii \(a\) and \(b\) (where \(a < b\)). The inner shell carries a net charge \(+Q\) and the outer shell carries a net charge \(-Q\). Which of the following best describes the graph of the electric energy density \(u_E\) stored in the electric field as a function of radial distance \(r\) from the common center?

![A schematic cross-section of a spherical capacitor. Two concentric circular outlines represent two thin spherical shells centered at the origin. The inner circle has radius a and is labeled with a charge +Q. The outer circle has radius b and is labeled with a charge -Q. A radial line extends from the common center outward past the outer shell. Arrows point from the center to the inner shell labeled a, and from the center to the outer shell labeled b. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/spherical-capacitor-setup-1785830899-4tgIhV.jpg)

- **A.** It is zero for \(r < a\), proportional to \(\dfrac{1}{r^2}\) for \(a < r < b\), and zero for \(r > b\).
- **B.** It is zero for \(r < a\), proportional to \(\dfrac{1}{r^4}\) for \(a < r < b\), and zero for \(r > b\).
- **C.** It is zero for \(r < a\), proportional to \(\dfrac{1}{r}\) for \(a < r < b\), and zero for \(r > b\).
- **D.** It is zero for \(r < a\), a non-zero constant for \(a < r < b\), and zero for \(r > b\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118235/*