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title: "A small planar loop with magnetic dipole moment \\(\\vec{\\mu}\\) is placed in a uniform external magnetic field \\(\\vec{B}\\). Four orientations of the dipole moment relative to the magnetic field are considered:  Orientation 1: \\(\\vec{\\mu}\\) is parallel to \\(\\vec{B}\\) (\\(\\theta = 0^\\circ\\)) Orientation 2: \\(\\vec{\\mu}\\) is at an angle \\(\\theta = 120^\\circ\\) relative to \\(\\vec{B}\\) Orientation 3: \\(\\vec{\\mu}\\) is perpendicular to \\(\\vec{B}\\) (\\(\\theta = 90^\\circ\\)) Orientation 4: \\(\\vec{\\mu}\\) is antiparallel to \\(\\vec{B}\\) (\\(\\theta = 180^\\circ\\))  Which of the following correctly ranks the orientations based on the magnetic potential energy \\(U\\) of the dipole-field system, from least to greatest?"
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url: "https://nerd-notes.com/ubq/121207/"
date_modified: "2026-08-23T04:58:51+00:00"
---

# A small planar loop with magnetic dipole moment \(\vec{\mu}\) is placed in a uniform external magnetic field \(\vec{B}\). Four orientations of the dipole moment relative to the magnetic field are considered:

Orientation 1: \(\vec{\mu}\) is parallel to \(\vec{B}\) (\(\theta = 0^\circ\))
Orientation 2: \(\vec{\mu}\) is at an angle \(\theta = 120^\circ\) relative to \(\vec{B}\)
Orientation 3: \(\vec{\mu}\) is perpendicular to \(\vec{B}\) (\(\theta = 90^\circ\))
Orientation 4: \(\vec{\mu}\) is antiparallel to \(\vec{B}\) (\(\theta = 180^\circ\))

Which of the following correctly ranks the orientations based on the magnetic potential energy \(U\) of the dipole-field system, from least to greatest?

A small planar loop with magnetic dipole moment \(\vec{\mu}\) is placed in a uniform external magnetic field \(\vec{B}\). Four orientations of the dipole moment relative to the magnetic field are considered:

Orientation 1: \(\vec{\mu}\) is parallel to \(\vec{B}\) (\(\theta = 0^\circ\))
Orientation 2: \(\vec{\mu}\) is at an angle \(\theta = 120^\circ\) relative to \(\vec{B}\)
Orientation 3: \(\vec{\mu}\) is perpendicular to \(\vec{B}\) (\(\theta = 90^\circ\))
Orientation 4: \(\vec{\mu}\) is antiparallel to \(\vec{B}\) (\(\theta = 180^\circ\))

Which of the following correctly ranks the orientations based on the magnetic potential energy \(U\) of the dipole-field system, from least to greatest?

![Four separate horizontally arranged square panels labeled 1, 2, 3, and 4 from left to right. In each panel, three identical horizontal gray arrows point to the right, representing a uniform magnetic field labeled \vec{B}. In Panel 1, a single solid black arrow labeled \vec{\mu} points horizontally to the right. In Panel 2, a single solid black arrow labeled \vec{\mu} starts at the center and points up and to the left at an angle of 120^\circ relative to the rightward horizontal. In Panel 3, a single solid black arrow labeled \vec{\mu} points vertically upward. In Panel 4, a single solid black arrow labeled \vec{\mu} points horizontally to the left. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461131-AH1Dle.jpg)

- **A.** \(U_4 < U_2 < U_3 < U_1\)
- **B.** \(U_1 < U_3 < U_2 < U_4\)
- **C.** \(U_1 < U_2 < U_3 < U_4\)
- **D.** \(U_3 < U_1 < U_2 < U_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121207/*