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title: "Two point charges, \\(q_1\\) and \\(q_2\\), are fixed on the \\(x\\)-axis at \\(x = 0\\) and \\(x = 3.0\\text{ m}\\), respectively. The accompanying graph shows the resulting electric field component \\(E_x\\) along the \\(x\\)-axis, where \\(E_x > 0\\) corresponds to an electric field directed in the \\(+x\\)-direction. The field diverges toward \\(+\\infty\\) immediately to the right of each charge and toward \\(-\\infty\\) immediately to the left, and it crosses zero at \\(x = 2.0\\text{ m}\\). Based on the graph, which of the following statements correctly identifies the signs and relative magnitudes of the two charges?"
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url: "https://nerd-notes.com/ubq/124701/"
date_modified: "2026-09-28T14:09:09+00:00"
---

# Two point charges, \(q_1\) and \(q_2\), are fixed on the \(x\)-axis at \(x = 0\) and \(x = 3.0\text{ m}\), respectively. The accompanying graph shows the resulting electric field component \(E_x\) along the \(x\)-axis, where \(E_x > 0\) corresponds to an electric field directed in the \(+x\)-direction. The field diverges toward \(+\infty\) immediately to the right of each charge and toward \(-\infty\) immediately to the left, and it crosses zero at \(x = 2.0\text{ m}\). Based on the graph, which of the following statements correctly identifies the signs and relative magnitudes of the two charges?

Two point charges, \(q_1\) and \(q_2\), are fixed on the \(x\)-axis at \(x = 0\) and \(x = 3.0\text{ m}\), respectively. The accompanying graph shows the resulting electric field component \(E_x\) along the \(x\)-axis, where \(E_x > 0\) corresponds to an electric field directed in the \(+x\)-direction. The field diverges toward \(+\infty\) immediately to the right of each charge and toward \(-\infty\) immediately to the left, and it crosses zero at \(x = 2.0\text{ m}\). Based on the graph, which of the following statements correctly identifies the signs and relative magnitudes of the two charges?

![A quantitative Cartesian plot with horizontal axis labeled \(x\text{ (m)}\) and vertical axis labeled \(E_x\). Ticks on the horizontal axis are marked at \(-1\), \(0\), \(1\), \(2\), \(3\), and \(4\). Vertical dashed lines represent asymptotes at \(x = 0\) and \(x = 3\). A single solid curve is plotted in three separate segments: for \(x < 0\), the curve lies entirely below the horizontal axis, starting near \(E_x = 0\) at the far left and curving downward toward \(-\infty\) as it approaches \(x = 0\); for \(0 < x < 3\), the curve descends from \(+\infty\) immediately to the right of \(x = 0\), passes through zero at exactly \(x = 2\), and continues downward toward \(-\infty\) as it approaches \(x = 3\); for \(x > 3\), the curve descends from \(+\infty\) immediately to the right of \(x = 3\) and flattens out toward the horizontal axis as \(x\) increases. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604549-4PivsL.jpg)

- **A.** The charges have opposite signs with \(q_1 = -2q_2\), because \(E_x\) changes sign between \(x = 0\) and \(x = 3.0\text{ m}\), and the zero-crossing is twice as far from \(x = 0\) as from \(x = 3.0\text{ m}\).
- **B.** Both charges are positive with \(q_1 = +4q_2\), because the field directs away from each charge on both sides, and the fields balance where the ratio of squared distances from the charges is \(4\).
- **C.** Both charges are positive with \(q_1 = +2q_2\), because the field directs away from each charge on both sides, and the zero-crossing is located at twice the distance from \(x = 0\) as from \(x = 3.0\text{ m}\).
- **D.** The charges have opposite signs with \(q_1 = -4q_2\), because \(E_x\) has opposite signs on either side of the zero-crossing at \(x = 2.0\text{ m}\), and the square of the distance from \(x = 0\) is four times that from \(x = 3.0\text{ m}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124701/*