---
title: "Two point charges, each with charge \\(+Q\\), are fixed on the y-axis at \\(y = +a\\) and \\(y = -a\\). Point P is located on the positive x-axis at a distance \\(x = d\\) from the origin, as shown in Figure 1."
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url: "https://nerd-notes.com/ubq/117840/"
date_modified: "2026-08-04T07:59:10+00:00"
---

# Two point charges, each with charge \(+Q\), are fixed on the y-axis at \(y = +a\) and \(y = -a\). Point P is located on the positive x-axis at a distance \(x = d\) from the origin, as shown in Figure 1.

Two point charges, each with charge \(+Q\), are fixed on the y-axis at \(y = +a\) and \(y = -a\). Point P is located on the positive x-axis at a distance \(x = d\) from the origin, as shown in Figure 1.

![A 2D Cartesian coordinate system with a vertical y-axis and horizontal x-axis. A point charge represented by a circle labeled '+Q' is located at y = +a, and a second identical point charge labeled '+Q' is located at y = -a. A point labeled 'P' is marked on the positive x-axis at x = d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830349-MTwXbo.jpg)

**Part a)** **Derive** an expression for the total electric potential \(V\) at point P due to the two point charges. Express your answer in terms of \(Q\), \(a\), \(d\), and physical constants, as appropriate. *(2 points)*

**Part b)** A third point charge \(-q\) with mass \(m\) is released from rest at point P. *(5 points)*

**Part c)** The two point charges \(+Q\) are removed. A thin, nonconducting rod of length \(2a\) and total charge \(+2Q\) is placed along the y-axis from \(y = -a\) to \(y = +a\), as shown in Figure 2. **Write**, but do not evaluate, an integral expression that can be used to calculate the electric potential at point P due to the rod. Express your answer in terms of \(Q\), \(a\), \(d\), and physical constants, as appropriate. *(3 points)*

**Part d)** **Indicate** how the electric potential at point P due to the rod compares to the electric potential at point P due to the two point charges found in part (a). - [ ] The potential due to the rod is greater. - [ ] The potential due to the two point charges is greater. - [ ] The potentials are equal. **Justify** your answer. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117840/*