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title: "Two identical circular wire loops of radius \\(R\\) are positioned coaxially along the \\(z\\)-axis, centered at \\(z = -R\\) and \\(z = +R\\), as shown. The loops carry equal currents \\(I\\) in opposite directions, such that the loop at \\(z = -R\\) produces an axial magnetic field in the \\(+z\\)-direction at its center, while the loop at \\(z = +R\\) produces an axial magnetic field in the \\(-z\\)-direction at its center. Four points on the \\(z\\)-axis are identified: Point \\(W\\) at \\(z = -R\\), Point \\(X\\) at \\(z = 0\\), Point \\(Y\\) at \\(z = +R\\), and Point \\(Z\\) at \\(z = +2R\\). Which of the following correctly ranks the magnitude of the net magnetic field \\(B\\) at these four points?"
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url: "https://nerd-notes.com/ubq/124810/"
date_modified: "2026-09-28T14:11:25+00:00"
---

# Two identical circular wire loops of radius \(R\) are positioned coaxially along the \(z\)-axis, centered at \(z = -R\) and \(z = +R\), as shown. The loops carry equal currents \(I\) in opposite directions, such that the loop at \(z = -R\) produces an axial magnetic field in the \(+z\)-direction at its center, while the loop at \(z = +R\) produces an axial magnetic field in the \(-z\)-direction at its center. Four points on the \(z\)-axis are identified: Point \(W\) at \(z = -R\), Point \(X\) at \(z = 0\), Point \(Y\) at \(z = +R\), and Point \(Z\) at \(z = +2R\). Which of the following correctly ranks the magnitude of the net magnetic field \(B\) at these four points?

Two identical circular wire loops of radius \(R\) are positioned coaxially along the \(z\)-axis, centered at \(z = -R\) and \(z = +R\), as shown. The loops carry equal currents \(I\) in opposite directions, such that the loop at \(z = -R\) produces an axial magnetic field in the \(+z\)-direction at its center, while the loop at \(z = +R\) produces an axial magnetic field in the \(-z\)-direction at its center. Four points on the \(z\)-axis are identified: Point \(W\) at \(z = -R\), Point \(X\) at \(z = 0\), Point \(Y\) at \(z = +R\), and Point \(Z\) at \(z = +2R\). Which of the following correctly ranks the magnitude of the net magnetic field \(B\) at these four points?

![A horizontal dashed line represents the z-axis, oriented horizontally with an arrow pointing to the right labeled z. Two identical circular wire loops of radius R are shown in oblique perspective as vertically oriented ellipses centered on the z-axis. The left loop is centered at a tick mark labeled -R, and the right loop is centered at a tick mark labeled R. The origin is marked by a tick labeled 0 midway between the loops. A tick mark to the right of the right loop is labeled 2R. Curved arrows on the perimeters of the two loops indicate opposite current directions, both labeled I. Four solid black dots on the z-axis mark specific points: dot W at z = -R, dot X at z = 0, dot Y at z = R, and dot Z at z = 2R. A vertical radial line segment from the center of the left loop to its top rim is labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604685-n46Lb7.jpg)

- **A.** \(B_X > B_W = B_Y > B_Z\)
- **B.** \(B_W = B_Y > B_X > B_Z\)
- **C.** \(B_W = B_Y > B_Z > B_X\)
- **D.** \(B_Z > B_W = B_Y > B_X\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124810/*