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title: "Two positive point charges, \\(q_1 = Q\\) and \\(q_2 = \\beta Q\\) (where \\(\\beta > 1\\) is a dimensionless constant), are fixed on the \\(x\\)-axis at \\(x = 0\\) and \\(x = d\\), respectively. A third positive point charge \\(+q\\) is placed on the \\(x\\)-axis between \\(q_1\\) and \\(q_2\\) in the region \\(0 < x < d\\). At what position \\(x\\) is the net electrostatic force on \\(+q\\) equal to zero?"
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url: "https://nerd-notes.com/ubq/117908/"
date_modified: "2026-08-04T08:02:32+00:00"
---

# Two positive point charges, \(q_1 = Q\) and \(q_2 = \beta Q\) (where \(\beta > 1\) is a dimensionless constant), are fixed on the \(x\)-axis at \(x = 0\) and \(x = d\), respectively. A third positive point charge \(+q\) is placed on the \(x\)-axis between \(q_1\) and \(q_2\) in the region \(0 < x < d\). At what position \(x\) is the net electrostatic force on \(+q\) equal to zero?

Two positive point charges, \(q_1 = Q\) and \(q_2 = \beta Q\) (where \(\beta > 1\) is a dimensionless constant), are fixed on the \(x\)-axis at \(x = 0\) and \(x = d\), respectively. A third positive point charge \(+q\) is placed on the \(x\)-axis between \(q_1\) and \(q_2\) in the region \(0 < x < d\). At what position \(x\) is the net electrostatic force on \(+q\) equal to zero?

![A horizontal x-axis with a origin labeled x = 0 and a point labeled x = d. At x = 0, a small filled circle represents charge q_1 = Q. At x = d, a larger filled circle represents charge q_2 = \beta Q. Between x = 0 and x = d, at coordinate x, a third filled circle represents charge +q. Two opposing horizontal vector arrows originate from charge +q: one pointing left toward x = 0 labeled \vec{F}_1 and one pointing right toward x = d labeled \vec{F}_2. A dimension line below the axis marks distance x from x = 0 to +q, and another dimension line marks the total distance d from x = 0 to x = d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830552-mV2E2V.jpg)

- **A.** \(x = \dfrac{d}{1 + \beta}\)
- **B.** \(x = \dfrac{d}{\sqrt{1 + \beta}}\)
- **C.** \(x = \dfrac{d}{1 + \sqrt{\beta}}\)
- **D.** \(x = \dfrac{d\sqrt{\beta}}{1 + \sqrt{\beta}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117908/*