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title: "Three independent experimental setups (X, Y, and Z) each consist of two long, parallel horizontal wires of length \\(L\\) suspended vertically from a ceiling by light insulating strings of length \\(d\\). In each setup, the wires carry steady currents in opposite directions, causing them to magnetically repel and hang in static equilibrium at small deflection angles relative to the vertical. The properties of the wires in each setup are given in the table below: | Setup | Wire | Current | Mass | Deflection Angle | |——-|——|———|——|——————| | X | Wire 1 | \\(I_0\\) | \\(m_0\\) | \\(\\theta_1\\) | | X | Wire 2 | \\(I_0\\) | \\(m_0\\) | \\(\\theta_2\\) | | Y | Wire 3 | \\(2I_0\\) | \\(m_0\\) | \\(\\theta_3\\) | | Y | Wire 4 | \\(I_0\\) | \\(m_0\\) | \\(\\theta_4\\) | | Z | Wire 5 | \\(2I_0\\) | \\(2m_0\\) | \\(\\theta_5\\) | | Z | Wire 6 | \\(2I_0\\) | \\(2m_0\\) | \\(\\theta_6\\) | Which of the following correctly ranks the equilibrium deflection angles \\(\\theta_1\\), \\(\\theta_3\\), \\(\\theta_4\\), and \\(\\theta_5\\)?"
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url: "https://nerd-notes.com/ubq/116457/"
date_modified: "2026-08-03T12:24:02+00:00"
---

# Three independent experimental setups (X, Y, and Z) each consist of two long, parallel horizontal wires of length \(L\) suspended vertically from a ceiling by light insulating strings of length \(d\). In each setup, the wires carry steady currents in opposite directions, causing them to magnetically repel and hang in static equilibrium at small deflection angles relative to the vertical. The properties of the wires in each setup are given in the table below: | Setup | Wire | Current | Mass | Deflection Angle | |——-|——|———|——|——————| | X | Wire 1 | \(I_0\) | \(m_0\) | \(\theta_1\) | | X | Wire 2 | \(I_0\) | \(m_0\) | \(\theta_2\) | | Y | Wire 3 | \(2I_0\) | \(m_0\) | \(\theta_3\) | | Y | Wire 4 | \(I_0\) | \(m_0\) | \(\theta_4\) | | Z | Wire 5 | \(2I_0\) | \(2m_0\) | \(\theta_5\) | | Z | Wire 6 | \(2I_0\) | \(2m_0\) | \(\theta_6\) | Which of the following correctly ranks the equilibrium deflection angles \(\theta_1\), \(\theta_3\), \(\theta_4\), and \(\theta_5\)?

Three independent experimental setups (X, Y, and Z) each consist of two long, parallel horizontal wires of length \(L\) suspended vertically from a ceiling by light insulating strings of length \(d\). In each setup, the wires carry steady currents in opposite directions, causing them to magnetically repel and hang in static equilibrium at small deflection angles relative to the vertical. The properties of the wires in each setup are given in the table below: | Setup | Wire | Current | Mass | Deflection Angle | |-------|------|---------|------|------------------| | X | Wire 1 | \(I_0\) | \(m_0\) | \(\theta_1\) | | X | Wire 2 | \(I_0\) | \(m_0\) | \(\theta_2\) | | Y | Wire 3 | \(2I_0\) | \(m_0\) | \(\theta_3\) | | Y | Wire 4 | \(I_0\) | \(m_0\) | \(\theta_4\) | | Z | Wire 5 | \(2I_0\) | \(2m_0\) | \(\theta_5\) | | Z | Wire 6 | \(2I_0\) | \(2m_0\) | \(\theta_6\) | Which of the following correctly ranks the equilibrium deflection angles \(\theta_1\), \(\theta_3\), \(\theta_4\), and \(\theta_5\)?

![A cross-sectional end-view diagram showing two long parallel wires suspended from a horizontal ceiling by two thin insulating strings of length d. The wires hang repelled apart from each other at a small angle theta relative to a vertical dashed center line. Wire 1 on the left and Wire 2 on the right are represented by small circles with current symbols inside. Two equal tension force vectors point up along the strings, gravitational force vectors point downward from the center of each wire, and horizontal magnetic repulsion force vectors point directly away from each other. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785759842-tgm9YP.jpg)

- **A.** \(\theta_3 > \theta_5 > \theta_4 > \theta_1\)
- **B.** (\(\theta_3 = \theta_4 = \theta_5) > \theta_1\)
- **C.** \(\theta_5 > \theta_3 > \theta_4 > \theta_1\)
- **D.** (\(\theta_3 = \theta_5) > (\theta_1 = \theta_4)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116457/*