---
title: "A rigid, straight wire segment of length \\(L\\) and mass \\(m_0\\) lies along the \\(x\\)-axis on a digital balance in a horizontal plane. A constant current \\(I\\) flows through the wire in the \\(+x\\)-direction. A standard right-handed Cartesian coordinate system is defined where the \\(+z\\)-axis points vertically upward and the \\(+y\\)-axis is horizontal and perpendicular to the wire. When a uniform magnetic field \\(\\vec{B}\\) is applied to the region containing the wire, the balance reading increases by an amount \\(\\Delta m\\). Which of the following correctly pairs the minimum magnitude \\(B_{\\text{min}}\\) of the magnetic field with the direction in which \\(\\vec{B}_{\\text{min}}\\) must point?"
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url: "https://nerd-notes.com/ubq/118604/"
date_modified: "2026-08-04T08:11:47+00:00"
---

# A rigid, straight wire segment of length \(L\) and mass \(m_0\) lies along the \(x\)-axis on a digital balance in a horizontal plane. A constant current \(I\) flows through the wire in the \(+x\)-direction. A standard right-handed Cartesian coordinate system is defined where the \(+z\)-axis points vertically upward and the \(+y\)-axis is horizontal and perpendicular to the wire. When a uniform magnetic field \(\vec{B}\) is applied to the region containing the wire, the balance reading increases by an amount \(\Delta m\). Which of the following correctly pairs the minimum magnitude \(B_{\text{min}}\) of the magnetic field with the direction in which \(\vec{B}_{\text{min}}\) must point?

A rigid, straight wire segment of length \(L\) and mass \(m_0\) lies along the \(x\)-axis on a digital balance in a horizontal plane. A constant current \(I\) flows through the wire in the \(+x\)-direction. A standard right-handed Cartesian coordinate system is defined where the \(+z\)-axis points vertically upward and the \(+y\)-axis is horizontal and perpendicular to the wire. When a uniform magnetic field \(\vec{B}\) is applied to the region containing the wire, the balance reading increases by an amount \(\Delta m\). Which of the following correctly pairs the minimum magnitude \(B_{\text{min}}\) of the magnetic field with the direction in which \(\vec{B}_{\text{min}}\) must point?

![A 3D perspective drawing of a rectangular digital scale sitting horizontally in the xy-plane. On top of the scale, a thin straight wire segment of length L lies along the x-axis. An arrow along the wire labeled I points in the positive x-direction. A standard right-handed 3D coordinate system is shown to the side, with the x-axis pointing to the right, the y-axis pointing horizontally into the page, and the z-axis pointing vertically upward. The digital display on the front of the scale shows a mass reading. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831106-vjzcYe.jpg)

- **A.** \(B_{\text{min}} = \dfrac{(m_0 + \Delta m)g}{I L}\) in the \(-y\)-direction
- **B.** \(B_{\text{min}} = \dfrac{\Delta m \text{ } g}{I L}\) in the \(+y\)-direction
- **C.** \(B_{\text{min}} = \dfrac{\Delta m \text{ } g}{I L}\) in the \(-z\)-direction
- **D.** \(B_{\text{min}} = \dfrac{\Delta m \text{ } g}{I L}\) in the \(-y\)-direction

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118604/*