---
title: "An infinite conducting slab of thickness \\(2d\\) is oriented parallel to the \\(xz\\)-plane and occupies the region \\(-d \\le y \\le d\\). A non-uniform volume current flows through the slab in the \\(+x\\)-direction (out of the page) with current density \\(\\vec{J} = J_0 \\left(\\dfrac{|y|}{d}\\right)\\hat{i}\\), where \\(J_0\\) is a positive constant. Which of the following expressions gives the magnitude of the magnetic field \\(B(y)\\) as a function of position \\(y\\) inside the region \\(0 \\le y \\le d\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/121268/"
date_modified: "2026-08-23T04:59:05+00:00"
---

# An infinite conducting slab of thickness \(2d\) is oriented parallel to the \(xz\)-plane and occupies the region \(-d \le y \le d\). A non-uniform volume current flows through the slab in the \(+x\)-direction (out of the page) with current density \(\vec{J} = J_0 \left(\dfrac{|y|}{d}\right)\hat{i}\), where \(J_0\) is a positive constant. Which of the following expressions gives the magnitude of the magnetic field \(B(y)\) as a function of position \(y\) inside the region \(0 \le y \le d\)?

An infinite conducting slab of thickness \(2d\) is oriented parallel to the \(xz\)-plane and occupies the region \(-d \le y \le d\). A non-uniform volume current flows through the slab in the \(+x\)-direction (out of the page) with current density \(\vec{J} = J_0 \left(\dfrac{|y|}{d}\right)\hat{i}\), where \(J_0\) is a positive constant. Which of the following expressions gives the magnitude of the magnetic field \(B(y)\) as a function of position \(y\) inside the region \(0 \le y \le d\)?

![A 2D cross-sectional diagram in the yz-plane showing a horizontal slab between horizontal solid boundary lines at y = d and y = -d. A horizontal dashed centerline marks y = 0. Inside the slab, current pointing out of the page is represented by encircled dots, with higher density near y = d and y = -d and zero density at y = 0. A dashed rectangular Amperian loop of horizontal width L and vertical span from -y to +y is centered on y = 0. A vertical y-axis points upward with tick marks at -d, -y, 0, y, and d. A horizontal z-axis points to the right. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461145-em1kQH.jpg)

- **A.** \(\dfrac{\mu_0 J_0 y^3}{3d^2}\)
- **B.** \(\dfrac{\mu_0 J_0 y^2}{4d}\)
- **C.** \(\dfrac{\mu_0 J_0 y^2}{d}\)
- **D.** \(\dfrac{\mu_0 J_0 y^2}{2d}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121268/*