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title: "A thin circular loop of radius \\(R\\) carries a steady current \\(I\\) and lies in the \\(xz\\)-plane centered at the origin, with the current circulating counterclockwise when viewed from the positive \\(y\\)-axis. An electron of mass \\(m\\) and charge \\(-e\\) is launched from the position \\((0, -y_0, 0)\\), where \\(y_0 > 0\\), with an initial velocity \\(\\vec{v} = v_0 \\hat{j}\\) directed along the positive \\(y\\)-axis toward the center of the loop. Gravitational effects are negligible. Which of the following correctly describes the magnetic force exerted on the electron and its resulting motion as it travels toward and through the center of the loop?"
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url: "https://nerd-notes.com/ubq/124865/"
date_modified: "2026-09-28T14:11:43+00:00"
---

# A thin circular loop of radius \(R\) carries a steady current \(I\) and lies in the \(xz\)-plane centered at the origin, with the current circulating counterclockwise when viewed from the positive \(y\)-axis. An electron of mass \(m\) and charge \(-e\) is launched from the position \((0, -y_0, 0)\), where \(y_0 > 0\), with an initial velocity \(\vec{v} = v_0 \hat{j}\) directed along the positive \(y\)-axis toward the center of the loop. Gravitational effects are negligible. Which of the following correctly describes the magnetic force exerted on the electron and its resulting motion as it travels toward and through the center of the loop?

A thin circular loop of radius \(R\) carries a steady current \(I\) and lies in the \(xz\)-plane centered at the origin, with the current circulating counterclockwise when viewed from the positive \(y\)-axis. An electron of mass \(m\) and charge \(-e\) is launched from the position \((0, -y_0, 0)\), where \(y_0 > 0\), with an initial velocity \(\vec{v} = v_0 \hat{j}\) directed along the positive \(y\)-axis toward the center of the loop. Gravitational effects are negligible. Which of the following correctly describes the magnetic force exerted on the electron and its resulting motion as it travels toward and through the center of the loop?

![A three-dimensional Cartesian coordinate frame with a vertical axis labeled y, a horizontal axis pointing right labeled x, and an axis pointing diagonally downward to the left labeled z, all intersecting at the origin. Centered at the origin in the horizontal xz-plane is an unshaded ellipse representing a circular loop of radius R. A single curved arrow along the front edge of the ellipse points in the direction of increasing x, labeled I. On the negative y-axis below the loop, a solid black dot represents an electron labeled -e. A single straight arrow originates at the dot and points vertically upward along the positive y-axis toward the origin, labeled \vec{v}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604703-xcrZNW.jpg)

- **A.** The magnetic force is non-zero and directed perpendicular to the \(y\)-axis, causing the electron to follow a helical path around the \(y\)-axis with decreasing radius as it approaches the origin.
- **B.** The magnetic force is directed in the \(-y\)-direction as the electron approaches the origin, causing it to move in a straight line along the \(y\)-axis while decelerating to a minimum speed at the origin.
- **C.** The magnetic force is zero at all points along the path, causing the electron to move in a straight line along the \(y\)-axis at constant speed.
- **D.** The magnetic force is directed radially outward from the \(y\)-axis, causing the electron to deflect away from the \(y\)-axis into the \(xy\)-plane while maintaining constant speed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124865/*