---
title: "A solid insulating sphere of radius \\(R\\) has a uniform volume charge density \\(\\rho_0\\). A spherical cavity of radius \\(b\\) (where \\(b < R\\)) is removed from the sphere, with its center located at position vector \\(\\vec{a}\\) relative to the sphere's center \\(O\\). Point \\(P\\) is located inside the cavity at position vector \\(\\vec{r}\\) relative to center \\(O\\). Which of the following expressions correctly gives the electric field vector \\(\\vec{E}\\) at point \\(P\\) inside the cavity?"
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url: "https://nerd-notes.com/ubq/118012/"
date_modified: "2026-08-04T08:02:54+00:00"
---

# A solid insulating sphere of radius \(R\) has a uniform volume charge density \(\rho_0\). A spherical cavity of radius \(b\) (where \(b < R\)) is removed from the sphere, with its center located at position vector \(\vec{a}\) relative to the sphere's center \(O\). Point \(P\) is located inside the cavity at position vector \(\vec{r}\) relative to center \(O\). Which of the following expressions correctly gives the electric field vector \(\vec{E}\) at point \(P\) inside the cavity?

A solid insulating sphere of radius \(R\) has a uniform volume charge density \(\rho_0\). A spherical cavity of radius \(b\) (where \(b < R\)) is removed from the sphere, with its center located at position vector \(\vec{a}\) relative to the sphere's center \(O\). Point \(P\) is located inside the cavity at position vector \(\vec{r}\) relative to center \(O\). Which of the following expressions correctly gives the electric field vector \(\vec{E}\) at point \(P\) inside the cavity?

![A large shaded circle of radius R represents a cross-section of an insulating sphere centered at point O. Inside this circle, toward the upper-right, a smaller unshaded circle of radius b represents a spherical cavity centered at point O'. A straight vector arrow labeled \(\vec{a}\) begins at center O and ends at cavity center O'. Inside the unshaded cavity circle, a black point is labeled P. A second vector arrow labeled \(\vec{r}\) begins at center O and ends at point P. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830574-IaNf29.jpg)

- **A.** \(\dfrac{\rho_0 \vec{r}}{3\varepsilon_0}\)
- **B.** \(\dfrac{\rho_0 (\vec{r} - \vec{a})}{3\varepsilon_0}\)
- **C.** \(\dfrac{\rho_0 (\vec{r} + \vec{a})}{3\varepsilon_0}\)
- **D.** \(\dfrac{\rho_0 \vec{a}}{3\varepsilon_0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118012/*