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title: "Two long, straight, parallel wires are oriented perpendicular to the xy-plane and carry constant currents in opposite directions. Wire 1 carries current \\(I\\) out of the page at \\((x, y) = (-d, 0)\\), and Wire 2 carries current \\(2I\\) into the page at \\((x, y) = (d, 0)\\). A magnetic field sensor moved along the x-axis measures the net magnetic field \\(\\vec{B}\\) and detects that it does not vanish at any point in the interval \\(-d < x < d\\), but drops to zero at exactly one location in the region \\(x < -d\\). Which of the following correctly explains these measurements?"
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url: "https://nerd-notes.com/ubq/121241/"
date_modified: "2026-08-23T04:58:59+00:00"
---

# Two long, straight, parallel wires are oriented perpendicular to the xy-plane and carry constant currents in opposite directions. Wire 1 carries current \(I\) out of the page at \((x, y) = (-d, 0)\), and Wire 2 carries current \(2I\) into the page at \((x, y) = (d, 0)\). A magnetic field sensor moved along the x-axis measures the net magnetic field \(\vec{B}\) and detects that it does not vanish at any point in the interval \(-d < x < d\), but drops to zero at exactly one location in the region \(x < -d\). Which of the following correctly explains these measurements?

Two long, straight, parallel wires are oriented perpendicular to the xy-plane and carry constant currents in opposite directions. Wire 1 carries current \(I\) out of the page at \((x, y) = (-d, 0)\), and Wire 2 carries current \(2I\) into the page at \((x, y) = (d, 0)\). A magnetic field sensor moved along the x-axis measures the net magnetic field \(\vec{B}\) and detects that it does not vanish at any point in the interval \(-d < x < d\), but drops to zero at exactly one location in the region \(x < -d\). Which of the following correctly explains these measurements?

![A horizontal x-axis with a central origin labeled 0. On the axis, at position -d, a circle containing a central dot represents a wire carrying current I out of the page, labeled Wire 1. At position +d on the axis, an identical circle containing a central cross represents a wire carrying current 2I into the page, labeled Wire 2. A vertical dashed line passes through the origin representing the y-axis. A horizontal axis arrow labeled +x points to the right, and a vertical axis arrow labeled +y points upward. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461139-uCBNmS.jpg)

- **A.** Between the wires, the fields from the two currents point in opposite directions along the y-axis but have unequal magnitudes, preventing cancellation. In the region \(x > d\), the field vectors point in opposing directions and achieve equal magnitudes because the faster decay of the field from the larger current allows the weaker current to balance it at large distances.
- **B.** Between the wires, magnetic field lines circulate in opposite senses and destructively interfere, resulting in a nonzero field everywhere except at a single saddle point off the x-axis. In the region \(x < -d\), the two field vectors point in the same direction, and their scalar sum vanishes where the magnetic vector potential reaches zero.
- **C.** Between the wires, the right-hand rule indicates that the field contributions oppose one another along the y-axis, leaving a net field due to the current imbalance. In the region \(x < -d\), the fields point in opposite directions and cancel because the field of a long wire scales inversely with the square of distance, allowing the smaller current to balance the larger current.
- **D.** Between the wires, the right-hand rule indicates that both currents produce magnetic fields oriented in the \(+y\)-direction, so their vector contributions add constructively. In the region \(x < -d\), the two fields point in opposite directions and cancel because the shorter distance to the smaller current balances the larger current located at a greater distance.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121241/*