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title: "A rigid, planar circular loop of wire carrying a constant steady current \\(I\\) is placed in an external non-uniform magnetic field \\(\\vec{B}\\). The loop experiences a net translational force. Which of the following best explains why the loop experiences a net translational force in this non-uniform field, whereas the same loop in a uniform magnetic field experiences zero net translational force?"
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url: "https://nerd-notes.com/ubq/118513/"
date_modified: "2026-08-04T08:11:12+00:00"
---

# A rigid, planar circular loop of wire carrying a constant steady current \(I\) is placed in an external non-uniform magnetic field \(\vec{B}\). The loop experiences a net translational force. Which of the following best explains why the loop experiences a net translational force in this non-uniform field, whereas the same loop in a uniform magnetic field experiences zero net translational force?

A rigid, planar circular loop of wire carrying a constant steady current \(I\) is placed in an external non-uniform magnetic field \(\vec{B}\). The loop experiences a net translational force. Which of the following best explains why the loop experiences a net translational force in this non-uniform field, whereas the same loop in a uniform magnetic field experiences zero net translational force?

![A circular wire loop carrying a steady current I (indicated by a clockwise arrow around the loop when viewed from the right) is positioned along the z-axis in a diverging magnetic field. Magnetic field lines, labeled B, enter from the left as parallel horizontal lines, then spread outward symmetrically to the top-right and bottom-right as they pass through the loop. On the top segment of the loop, a magnetic field vector points up and right, yielding an upward-right force vector dF. On the bottom segment, a magnetic field vector points down and right, yielding a downward-right force vector dF. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831072-aublri.jpg)

- **A.** In a non-uniform field, the magnetic field gradient produces an unequal distribution of charge carriers along the wire, causing the current \(I\) to vary in magnitude at different points around the loop.
- **B.** In a uniform field, magnetic field lines form closed loops that exert equal inward magnetic pressure, whereas in a non-uniform field, the field lines terminate on the conductor.
- **C.** In a uniform field, the differential magnetic forces \(d\vec{F} = I\,d\vec{\ell} \times \vec{B}\) on opposite current elements of the loop have equal magnitudes and opposite directions, yielding a vector sum of zero; in a non-uniform field, the magnetic field vectors at opposite elements differ, preventing complete force cancellation.
- **D.** In a uniform field, magnetic forces act strictly perpendicular to the plane of the loop, whereas in a non-uniform field, magnetic forces act parallel to the plane of the loop.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118513/*