---
title: "A solid insulating sphere of radius \\(R\\) contains a non-uniform distribution of positive charge. The total charge enclosed within a concentric spherical surface of radius \\(r\\) (for \\(r \\le R\\)) is given by \\(q_{\\text{enc}}(r) = Q \\left(\\dfrac{r}{R}\\right)^4\\), where \\(Q\\) is the total charge of the sphere. Which of the following best describes the magnitude of the electric field \\(E\\) as a function of distance \\(r\\) from the center of the sphere for all \\(r \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/116973/"
date_modified: "2026-08-04T06:16:55+00:00"
---

# A solid insulating sphere of radius \(R\) contains a non-uniform distribution of positive charge. The total charge enclosed within a concentric spherical surface of radius \(r\) (for \(r \le R\)) is given by \(q_{\text{enc}}(r) = Q \left(\dfrac{r}{R}\right)^4\), where \(Q\) is the total charge of the sphere. Which of the following best describes the magnitude of the electric field \(E\) as a function of distance \(r\) from the center of the sphere for all \(r \ge 0\)?

A solid insulating sphere of radius \(R\) contains a non-uniform distribution of positive charge. The total charge enclosed within a concentric spherical surface of radius \(r\) (for \(r \le R\)) is given by \(q_{\text{enc}}(r) = Q \left(\dfrac{r}{R}\right)^4\), where \(Q\) is the total charge of the sphere. Which of the following best describes the magnitude of the electric field \(E\) as a function of distance \(r\) from the center of the sphere for all \(r \ge 0\)?

- **A.** For \(r \le R\), \(E\) increases linearly with \(r\); for \(r > R\), \(E\) decreases as \(\dfrac{1}{r^2}\); the electric field is continuous at \(r = R\).
- **B.** For \(r \le R\), \(E\) increases quadratically with \(r\); for \(r > R\), \(E\) remains constant at a non-zero value; the electric field is discontinuous at \(r = R\).
- **C.** For \(r \le R\), \(E\) increases quadratically with \(r\); for \(r > R\), \(E\) decreases as \(\dfrac{1}{r^2}\); the electric field is continuous at \(r = R\).
- **D.** For \(r \le R\), \(E\) increases as \(r^4\); for \(r > R\), \(E\) decreases linearly with \(r\); the electric field is discontinuous at \(r = R\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116973/*