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title: "A point charge \\(+Q\\) is fixed at the center of an uncharged, hollow conducting spherical shell with inner radius \\(R_1\\) and outer radius \\(R_2\\), as shown in the cross-sectional diagram. Two concentric spherical Gaussian surfaces are considered: surface \\(S_{\\text{bulk}}\\) of radius \\(r_1\\) located within the conducting material (\\(R_1 < r_1  R_2\\)). The system has reached electrostatic equilibrium. Which of the following correctly pairs the net electric flux through these Gaussian surfaces with the fate of the electric field lines that originate from the charge \\(+Q\\)?"
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url: "https://nerd-notes.com/ubq/124719/"
date_modified: "2026-09-28T14:09:18+00:00"
---

# A point charge \(+Q\) is fixed at the center of an uncharged, hollow conducting spherical shell with inner radius \(R_1\) and outer radius \(R_2\), as shown in the cross-sectional diagram. Two concentric spherical Gaussian surfaces are considered: surface \(S_{\text{bulk}}\) of radius \(r_1\) located within the conducting material (\(R_1 < r_1  R_2\)). The system has reached electrostatic equilibrium. Which of the following correctly pairs the net electric flux through these Gaussian surfaces with the fate of the electric field lines that originate from the charge \(+Q\)?

A point charge \(+Q\) is fixed at the center of an uncharged, hollow conducting spherical shell with inner radius \(R_1\) and outer radius \(R_2\), as shown in the cross-sectional diagram. Two concentric spherical Gaussian surfaces are considered: surface \(S_{\text{bulk}}\) of radius \(r_1\) located within the conducting material (\(R_1 < r_1 < R_2\)), and surface \(S_{\text{ext}}\) of radius \(r_2\) located outside the shell (\(r_2 > R_2\)). The system has reached electrostatic equilibrium. Which of the following correctly pairs the net electric flux through these Gaussian surfaces with the fate of the electric field lines that originate from the charge \(+Q\)?

![A cross-sectional view of concentric circles centered at a common origin. At the center is a solid black dot labeled \(+Q\). Surrounding the dot is a solid circle of radius \(R_1\) representing the inner boundary of a shell, and a larger concentric solid circle of radius \(R_2\) representing the outer boundary. The annular region between the solid circles of radius \(R_1\) and \(R_2\) has light gray diagonal cross-hatch shading. Two dashed concentric circles represent Gaussian surfaces: a dashed circle of radius \(r_1\) located in the shaded annular region, labeled \(S_{\text{bulk}}\) with a small pointer line, and a larger dashed circle of radius \(r_2\) outside the outer solid circle, labeled \(S_{\text{ext}}\) with a small pointer line. A horizontal dashed centerline extends from the central dot to the right, with two dimension arrows pointing to the solid circle boundaries labeled \(R_1\) and \(R_2\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604557-QMCFnj.jpg)

- **A.** Net flux: \(\Phi_{\text{bulk}} = \dfrac{Q}{\varepsilon_0}\) and \(\Phi_{\text{ext}} = \dfrac{Q}{\varepsilon_0}\) ; Field lines from \(+Q\): Pass continuously through the shell into the region \(r > R_2\)
- **B.** Net flux: \(\Phi_{\text{bulk}} = \dfrac{Q}{\varepsilon_0}\) and \(\Phi_{\text{ext}} = \dfrac{Q}{\varepsilon_0}\) ; Field lines from \(+Q\): Terminate on the inner surface at \(r = R_1\)
- **C.** Net flux: \(\Phi_{\text{bulk}} = 0\) and \(\Phi_{\text{ext}} = \dfrac{Q}{\varepsilon_0}\) ; Field lines from \(+Q\): Pass continuously through the shell into the region \(r > R_2\)
- **D.** Net flux: \(\Phi_{\text{bulk}} = 0\) and \(\Phi_{\text{ext}} = \dfrac{Q}{\varepsilon_0}\) ; Field lines from \(+Q\): Terminate on the inner surface at \(r = R_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124719/*