---
title: "Two very long, straight, parallel conducting wires, Wire 1 and Wire 2, are fixed in place on a horizontal nonconducting table. The wires are separated by a distance \\( d \\). Wire 1 carries a constant current \\( I_1 \\) toward the top of the page. Wire 2 carries a constant current \\( I_2 \\) also toward the top of the page."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117728/"
date_modified: "2026-08-04T07:54:07+00:00"
---

# Two very long, straight, parallel conducting wires, Wire 1 and Wire 2, are fixed in place on a horizontal nonconducting table. The wires are separated by a distance \( d \). Wire 1 carries a constant current \( I_1 \) toward the top of the page. Wire 2 carries a constant current \( I_2 \) also toward the top of the page.

Two very long, straight, parallel conducting wires, Wire 1 and Wire 2, are fixed in place on a horizontal nonconducting table. The wires are separated by a distance \( d \). Wire 1 carries a constant current \( I_1 \) toward the top of the page. Wire 2 carries a constant current \( I_2 \) also toward the top of the page.

![A flat 2D top-down view of two long vertical parallel lines representing wires. The left wire is labeled \( \text{Wire 1} \) and the right wire is labeled \( \text{Wire 2} \). A horizontal dashed line connects the two wires near their centers, with the label \( d \) placed centered above the dashed line. On Wire 1, a vertical arrow points straight toward the top of the image, labeled \( I_1 \). On Wire 2, a vertical arrow points straight toward the top of the image, labeled \( I_2 \). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830047-bFgYIc.jpg)

**Part a)** **Indicate** the direction of the magnetic force exerted on Wire 2 by Wire 1. - [ ] Left (toward Wire 1) - [ ] Right (away from Wire 1) - [ ] Into the page - [ ] Out of the page **Justify** your answer using physical principles.

**Part b)** **Derive** an expression for the magnitude of the magnetic force per unit length, \( \dfrac{F_M}{L} \), exerted on Wire 2 by Wire 1. **Express** your answer in terms of \( I_1 \), \( I_2 \), \( d \), and fundamental constants.

**Part c)** A student makes the following claim: "If the direction of the current in Wire 2 is reversed so it flows toward the bottom of the page, the wires will repel each other. Furthermore, if the magnitude of \( I_2 \) is then doubled while \( I_1 \) remains unchanged, the repulsive force per unit length will quadruple." **Evaluate** this claim. **Explain** how the physical principles used in part (a) and the mathematical relationship derived in part (b) support or refute the qualitative and quantitative aspects of the student's claim.

**Part d)** Wire 2 is now slowly moved to the right so that the distance \( d \) between the wires increases. **Sketch** a graph of the magnitude of the magnetic force per unit length \( \dfrac{F_M}{L} \) exerted on Wire 2 as a function of the distance \( d \).


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117728/*