---
title: "An uncharged, solid conducting body of arbitrary outer shape contains an empty, irregularly shaped internal cavity. A point charge \\(+q\\) is fixed at a distance outside the conductor, and the system reaches electrostatic equilibrium. A student correctly asserts that the electric field is zero at every point inside the cavity. Which of the following best explains why the field inside the cavity is zero, and why Gauss’s law alone is insufficient to reach this conclusion?"
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url: "https://nerd-notes.com/ubq/118226/"
date_modified: "2026-08-04T08:08:15+00:00"
---

# An uncharged, solid conducting body of arbitrary outer shape contains an empty, irregularly shaped internal cavity. A point charge \(+q\) is fixed at a distance outside the conductor, and the system reaches electrostatic equilibrium. A student correctly asserts that the electric field is zero at every point inside the cavity. Which of the following best explains why the field inside the cavity is zero, and why Gauss’s law alone is insufficient to reach this conclusion?

An uncharged, solid conducting body of arbitrary outer shape contains an empty, irregularly shaped internal cavity. A point charge \(+q\) is fixed at a distance outside the conductor, and the system reaches electrostatic equilibrium. A student correctly asserts that the electric field is zero at every point inside the cavity. Which of the following best explains why the field inside the cavity is zero, and why Gauss's law alone is insufficient to reach this conclusion?

![An uncharged irregularly shaped conductor with an empty, irregularly shaped interior cavity. A single positive point charge labeled +q sits outside the conductor to the left. The conductor material is shaded light grey, while the cavity inside and the region outside are white. A dashed closed loop labeled C passes partly through the empty cavity space and partly through the shaded conducting material. No field lines or charge distributions appear inside the cavity.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830895-s2JSIS.jpg)

- **A.** Gauss's law only establishes that the net flux through a surface inside the cavity is zero, which permits non-uniform cavity surface charges. The field is zero because if field lines existed in the cavity, a closed path integral \(\oint \vec{E} \cdot d\vec{\ell}\) running along a field line and returning through the conducting material would be non-zero, violating the conservative nature of static fields.
- **B.** Gauss's law alone proves the field is zero because any Gaussian surface drawn within the empty cavity encloses zero net charge, and zero enclosed charge mathematically guarantees that the electric field magnitude must be zero at every point on that Gaussian surface regardless of geometry.
- **C.** The external charge \(+q\) induces an equal and opposite charge \(-q\) distributed over the cavity's inner surface, and the electric fields produced by these induced cavity charges cancel out at every internal point due to the principle of superposition.
- **D.** The mobile conduction electrons in the conductor rearrange to absorb and block external electric field lines at the outer boundary, physically preventing the field from penetrating the metal and entering the cavity region.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118226/*