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title: "The electric flux across three closed, irregularly shaped Gaussian surfaces, \\(S_1\\), \\(S_2\\), and \\(S_3\\), is measured in an electrostatic field. Surface \\(S_1\\) has an outward flux magnitude of \\(3\\Phi_0\\) and an inward flux magnitude of \\(2\\Phi_0\\), enclosing a net charge of \\(+Q_0\\). Surface \\(S_2\\) exhibits an outward flux magnitude of \\(\\Phi_0\\) and an inward flux magnitude of \\(4\\Phi_0\\), while surface \\(S_3\\) exhibits an outward flux magnitude of \\(4\\Phi_0\\), an inward flux magnitude of \\(6\\Phi_0\\), and encloses both a known charge \\(q_A = +3Q_0\\) and an unknown charge \\(q_B\\). Which of the following comparisons correctly identifies the net electric flux \\(\\Phi_{\\text{net}, 2}\\) through surface \\(S_2\\), the net electric flux \\(\\Phi_{\\text{net}, 3}\\) through surface \\(S_3\\), and the value of charge \\(q_B\\)?"
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url: "https://nerd-notes.com/ubq/124690/"
date_modified: "2026-09-28T14:09:06+00:00"
---

# The electric flux across three closed, irregularly shaped Gaussian surfaces, \(S_1\), \(S_2\), and \(S_3\), is measured in an electrostatic field. Surface \(S_1\) has an outward flux magnitude of \(3\Phi_0\) and an inward flux magnitude of \(2\Phi_0\), enclosing a net charge of \(+Q_0\). Surface \(S_2\) exhibits an outward flux magnitude of \(\Phi_0\) and an inward flux magnitude of \(4\Phi_0\), while surface \(S_3\) exhibits an outward flux magnitude of \(4\Phi_0\), an inward flux magnitude of \(6\Phi_0\), and encloses both a known charge \(q_A = +3Q_0\) and an unknown charge \(q_B\). Which of the following comparisons correctly identifies the net electric flux \(\Phi_{\text{net}, 2}\) through surface \(S_2\), the net electric flux \(\Phi_{\text{net}, 3}\) through surface \(S_3\), and the value of charge \(q_B\)?

The electric flux across three closed, irregularly shaped Gaussian surfaces, \(S_1\), \(S_2\), and \(S_3\), is measured in an electrostatic field. Surface \(S_1\) has an outward flux magnitude of \(3\Phi_0\) and an inward flux magnitude of \(2\Phi_0\), enclosing a net charge of \(+Q_0\). Surface \(S_2\) exhibits an outward flux magnitude of \(\Phi_0\) and an inward flux magnitude of \(4\Phi_0\), while surface \(S_3\) exhibits an outward flux magnitude of \(4\Phi_0\), an inward flux magnitude of \(6\Phi_0\), and encloses both a known charge \(q_A = +3Q_0\) and an unknown charge \(q_B\). Which of the following comparisons correctly identifies the net electric flux \(\Phi_{\text{net}, 2}\) through surface \(S_2\), the net electric flux \(\Phi_{\text{net}, 3}\) through surface \(S_3\), and the value of charge \(q_B\)?

![Three distinct closed irregular loop shapes arranged horizontally from left to right, labeled S_1, S_2, and S_3. Left surface S_1 contains a central point labeled +Q_0, with three outward-pointing arrows crossing its boundary and two inward-pointing arrows crossing its boundary. Middle surface S_2 has one outward-pointing arrow crossing its boundary and four inward-pointing arrows crossing its boundary. Right surface S_3 contains two distinct points in its interior labeled q_A and q_B, with four outward-pointing arrows crossing its boundary and six inward-pointing arrows crossing its boundary. All arrows have solid thin shafts with standard triangular heads indicating direction into or out of the closed boundary. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604545-MdyO5w.jpg)

- **A.** | \(\Phi_{\text{net}, 2} = -3\Phi_0\) | \(\Phi_{\text{net}, 3} = -2\Phi_0\) | \(q_B = -5Q_0\) |
- **B.** | \(\Phi_{\text{net}, 2} = +3\Phi_0\) | \(\Phi_{\text{net}, 3} = +2\Phi_0\) | \(q_B = -Q_0\) |
- **C.** | \(\Phi_{\text{net}, 2} = -3\Phi_0\) | \(\Phi_{\text{net}, 3} = -2\Phi_0\) | \(q_B = -2Q_0\) |
- **D.** | \(\Phi_{\text{net}, 2} = +5\Phi_0\) | \(\Phi_{\text{net}, 3} = +10\Phi_0\) | \(q_B = +7Q_0\) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124690/*