---
title: "An uncharged hollow conducting sphere with inner radius \\(a\\) and outer radius \\(b\\) surrounds an empty cavity. The conductor is in electrostatic equilibrium. A point charge \\(+Q\\) is fixed at a distance \\(d > b\\) from the center of the sphere. What are the electric field magnitude \\(E_{\\text{cav}}\\)"
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url: "https://nerd-notes.com/ubq/118231/"
date_modified: "2026-08-04T08:08:16+00:00"
---

# An uncharged hollow conducting sphere with inner radius \(a\) and outer radius \(b\) surrounds an empty cavity. The conductor is in electrostatic equilibrium. A point charge \(+Q\) is fixed at a distance \(d > b\) from the center of the sphere. What are the electric field magnitude \(E_{\text{cav}}\)

An uncharged hollow conducting sphere with inner radius \(a\) and outer radius \(b\) surrounds an empty cavity. The conductor is in electrostatic equilibrium. A point charge \(+Q\) is fixed at a distance \(d > b\) from the center of the sphere. What are the electric field magnitude \(E_{\text{cav}}\)

![A cross-sectional view of a thick hollow spherical conducting shell centered at the origin, with inner radius a and outer radius b. The region between r = a and r = b is shaded gray to represent conducting material. The central cavity region r < a is empty with a point labeled C at the center. To the right along the horizontal axis, at a distance d from center C where d > b, a small filled circle represents a point charge labeled +Q. No other labels, lines, or vectors appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830896-s0jr6k.jpg)

- **A.** \(E_{\text{cav}} = 0\) and \(Q_{\text{inner}} = 0\)
- **B.** \(E_{\text{cav}} = 0\) and \(Q_{\text{inner}} = -Q\)
- **C.** \(E_{\text{cav}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{d^2}\) and \(Q_{\text{inner}} = 0\)
- **D.** \(E_{\text{cav}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{d^2}\) and \(Q_{\text{inner}} = -Q\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118231/*