---
title: "A long, straight wire carrying a steady current \\(I\\) lies in the same plane as a right-triangular loop. The side of the loop of height \\(h\\) is parallel to the wire at a distance \\(a\\) from it. The base of the loop has length \\(b\\) and extends perpendicularly away from the wire, so that the vertex opposite the vertical side is at a distance \\(a + b\\) from the wire. Which of the following expressions is equal to the magnetic flux \\(\\Phi_B\\) through the triangular loop?"
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url: "https://nerd-notes.com/ubq/118664/"
date_modified: "2026-08-04T08:13:35+00:00"
---

# A long, straight wire carrying a steady current \(I\) lies in the same plane as a right-triangular loop. The side of the loop of height \(h\) is parallel to the wire at a distance \(a\) from it. The base of the loop has length \(b\) and extends perpendicularly away from the wire, so that the vertex opposite the vertical side is at a distance \(a + b\) from the wire. Which of the following expressions is equal to the magnetic flux \(\Phi_B\) through the triangular loop?

A long, straight wire carrying a steady current \(I\) lies in the same plane as a right-triangular loop. The side of the loop of height \(h\) is parallel to the wire at a distance \(a\) from it. The base of the loop has length \(b\) and extends perpendicularly away from the wire, so that the vertex opposite the vertical side is at a distance \(a + b\) from the wire. Which of the following expressions is equal to the magnetic flux \(\Phi_B\) through the triangular loop?

![A vertical line representing a long straight wire carries a current labeled I pointing upward. To the right of the wire, a right-triangular loop is drawn in the same plane. The vertical left edge of the triangle has height h and is parallel to the wire, positioned at a horizontal distance a from the wire. The horizontal bottom edge of the triangle has length b and extends from x = a to x = a + b along a horizontal axis perpendicular to the wire. The hypotenuse connects the top vertex (a, h) to the far-right vertex (a + b, 0). Arrowheads indicating horizontal dimensions show distance a from the wire to the vertical edge and distance b across the base. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831215-q4fTYM.jpg)

- **A.** \(\Phi_B = \dfrac{\mu_0 I h}{2\pi} \ln\left(\dfrac{a+b}{a}\right)\)
- **B.** \(\Phi_B = \dfrac{\mu_0 I h}{4\pi} \ln\left(\dfrac{a+b}{a}\right)\)
- **C.** \(\Phi_B = \dfrac{\mu_0 I h}{2\pi b} \left[ a \ln\left(\dfrac{a+b}{a}\right) - b \right]\)
- **D.** \(\Phi_B = \dfrac{\mu_0 I h}{2\pi b} \left[ (a+b)\ln\left(\dfrac{a+b}{a}\right) - b \right]\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118664/*