---
title: "A point charge \\(+q\\) is fixed at the center of an uncharged, thick spherical conducting shell with inner radius \\(a\\) and outer radius \\(b\\) in electrostatic equilibrium. Which of the following correctly pairs the magnitude of the electric field \\(E(r_1)\\) at a distance \\(r_1\\) from the center in the cavity (\\(0 < r_1 < a\\)) with the magnitude of the electric field \\(E(r_2)\\) at a distance \\(r_2\\) from the center inside the conducting material (\\(a < r_2 < b\\))?"
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url: "https://nerd-notes.com/ubq/117900/"
date_modified: "2026-08-04T08:02:30+00:00"
---

# A point charge \(+q\) is fixed at the center of an uncharged, thick spherical conducting shell with inner radius \(a\) and outer radius \(b\) in electrostatic equilibrium. Which of the following correctly pairs the magnitude of the electric field \(E(r_1)\) at a distance \(r_1\) from the center in the cavity (\(0 < r_1 < a\)) with the magnitude of the electric field \(E(r_2)\) at a distance \(r_2\) from the center inside the conducting material (\(a < r_2 < b\))?

A point charge \(+q\) is fixed at the center of an uncharged, thick spherical conducting shell with inner radius \(a\) and outer radius \(b\) in electrostatic equilibrium. Which of the following correctly pairs the magnitude of the electric field \(E(r_1)\) at a distance \(r_1\) from the center in the cavity (\(0 < r_1 < a\)) with the magnitude of the electric field \(E(r_2)\) at a distance \(r_2\) from the center inside the conducting material (\(a < r_2 < b\))?

![A cross-sectional schematic diagram showing a small central dot labeled +q. Surrounding the center dot is a thick circular ring representing a spherical shell, with inner boundary at radius a and outer boundary at radius b. The space between radius a and radius b is filled with light gray shading to represent conducting material. A dashed concentric circle of radius r_1 lies in the inner white cavity region (r_1 < a). A second dashed concentric circle of radius r_2 lies within the gray shaded region (a < r_2 < b). Four radial line segments with arrowheads originate at the central point charge, labeled a, b, r_1, and r_2 pointing to their respective boundaries and circles. No other labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830549-QCKNRN.jpg)

- **A.** \(E(r_1) = 0\) and \(E(r_2) = 0\)
- **B.** \(E(r_1) = 0\) and \(E(r_2) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r_2^2}\)
- **C.** \(E(r_1) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r_1^2}\) and \(E(r_2) = 0\)
- **D.** \(E(r_1) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r_1^2}\) and \(E(r_2) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r_2^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117900/*