---
title: "A thin, infinitely wide flat sheet lying in the \\(xy\\)-plane carries a uniform surface current density \\(\\vec{K} = K\\hat{i}\\), where \\(K\\) is constant. An Amperian loop can be used to evaluate the magnetic field produced by this current distribution at points not on the sheet. Which of the following correctly gives the direction of the magnetic field in the region \\(z > 0\\) and the magnitude \\(B\\) of the magnetic field on either side of the sheet?"
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url: "https://nerd-notes.com/ubq/118519/"
date_modified: "2026-08-04T08:11:13+00:00"
---

# A thin, infinitely wide flat sheet lying in the \(xy\)-plane carries a uniform surface current density \(\vec{K} = K\hat{i}\), where \(K\) is constant. An Amperian loop can be used to evaluate the magnetic field produced by this current distribution at points not on the sheet. Which of the following correctly gives the direction of the magnetic field in the region \(z > 0\) and the magnitude \(B\) of the magnetic field on either side of the sheet?

A thin, infinitely wide flat sheet lying in the \(xy\)-plane carries a uniform surface current density \(\vec{K} = K\hat{i}\), where \(K\) is constant. An Amperian loop can be used to evaluate the magnetic field produced by this current distribution at points not on the sheet. Which of the following correctly gives the direction of the magnetic field in the region \(z > 0\) and the magnitude \(B\) of the magnetic field on either side of the sheet?

![A flat rectangular surface representing a thin sheet lies in the xy-plane of a three-dimensional Cartesian coordinate system with origin O. The x-axis extends horizontally to the right, the y-axis extends into the page along a diagonal toward the upper-right, and the z-axis extends vertically upward. On the top face of the sheet, four parallel straight arrows point along the positive x-axis, each labeled K. A point on the positive z-axis above the sheet is labeled z > 0, and a point on the negative z-axis below the sheet is labeled z < 0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831072-PGqNQ9.jpg)

- **A.** Direction for \(z > 0\): \(-\hat{j}\) | Magnitude \(B\): \(\dfrac{1}{2}\mu_0 K\)
- **B.** Direction for \(z > 0\): \(-\hat{j}\) | Magnitude \(B\): \(\mu_0 K\)
- **C.** Direction for \(z > 0\): \(+\hat{j}\) | Magnitude \(B\): \(\dfrac{1}{2}\mu_0 K\)
- **D.** Direction for \(z > 0\): \(+\hat{j}\) | Magnitude \(B\): \(\mu_0 K\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118519/*