---
title: "A student is designing an experiment to investigate the magnetic field produced by a long, straight vertical wire. The student has a variable DC power supply, a switch, an ammeter, connecting wires, and a magnetic field probe that measures the component of the magnetic field perpendicular to its sensor face."
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url: "https://nerd-notes.com/ubq/117830/"
date_modified: "2026-08-04T07:58:57+00:00"
---

# A student is designing an experiment to investigate the magnetic field produced by a long, straight vertical wire. The student has a variable DC power supply, a switch, an ammeter, connecting wires, and a magnetic field probe that measures the component of the magnetic field perpendicular to its sensor face.

A student is designing an experiment to investigate the magnetic field produced by a long, straight vertical wire. The student has a variable DC power supply, a switch, an ammeter, connecting wires, and a magnetic field probe that measures the component of the magnetic field perpendicular to its sensor face.

**Part a)** **Draw** a schematic diagram of the circuit the student should construct to power the wire and measure the current flowing through it. Include the variable power supply, the straight wire, the ammeter, and the switch. Use standard circuit symbols. *(1 points)*

**Part b)** A top-down cross-sectional view of the vertical wire is shown below, with the current directed out of the page. **Draw** an "X" to indicate a location at a distance \( r \) from the center of the wire where the magnetic field probe could be placed. **Draw** an arrow originating at the "X" to indicate the orientation the probe's sensor should point to measure the maximum positive magnetic field produced by the wire. *(2 points)*

**Part c)** Use Ampère's law to **derive** an expression for the magnitude of the magnetic field \( B \) at a distance \( r \) from the center of the wire when it carries a current \( I \). *(2 points)*

**Part d)** The student sets the current to \( I = 10.0 \text{ A} \) and measures the magnetic field \( B \) at various distances \( r \). The data are shown in the table below. | \( r \text{ (m)} \) | \( B \text{ (mT)} \) |                 |                 | |:-------------------:|:--------------------:|:---------------:|:---------------:| | 0.010               | 0.25                 |                 |                 | | 0.020               | 0.15                 |                 |                 | | 0.030               | 0.12                 |                 |                 | | 0.040               | 0.10                 |                 |                 | | 0.050               | 0.09                 |                 |                 | **Indicate** which quantities should be graphed to yield a straight line whose slope could be used to calculate an experimental value for the magnetic permeability of free space, \( \mu_0 \). - Vertical axis: _______ - Horizontal axis: _______ *(1 points)*

**Part e)** Use the blank columns in the table to calculate and record values for the quantities identified in part (d). **Plot** the data points on the provided grid to represent the relationship. **Draw** a best-fit straight line. *(3 points)*

**Part f)** Use the slope of the best-fit line to **calculate** an experimental value for \( \mu_0 \). *(2 points)*

**Part g)** The student notices that the best-fit line does not pass through the origin. They correctly attribute this to the presence of Earth's magnetic field in the room. The student claims that as long as Earth's magnetic field is constant, its presence has a negligible effect on the accuracy of the value of \( \mu_0 \) calculated in part (f). **Justify** this claim. *(1 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117830/*