---
title: "An infinite planar slab of thickness \\(d\\) is aligned parallel to the \\(yz\\)-plane between \\(x = 0\\) and \\(x = d\\). The slab contains a non-uniform volume charge density \\(\\rho(x) = \\rho_0 \\sin\\left(\\dfrac{\\pi x}{d}\\right)\\) for \\(0 \\le x \\le d\\), where \\(\\rho_0\\) is a positive constant. Which of the following expressions gives the \\(x\\)-component of the electric field, \\(E_x(x)\\), inside the slab as a function of position \\(x\\) for \\(0 \\le x \\le d\\)?"
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url: "https://nerd-notes.com/ubq/117967/"
date_modified: "2026-08-04T08:02:43+00:00"
---

# An infinite planar slab of thickness \(d\) is aligned parallel to the \(yz\)-plane between \(x = 0\) and \(x = d\). The slab contains a non-uniform volume charge density \(\rho(x) = \rho_0 \sin\left(\dfrac{\pi x}{d}\right)\) for \(0 \le x \le d\), where \(\rho_0\) is a positive constant. Which of the following expressions gives the \(x\)-component of the electric field, \(E_x(x)\), inside the slab as a function of position \(x\) for \(0 \le x \le d\)?

An infinite planar slab of thickness \(d\) is aligned parallel to the \(yz\)-plane between \(x = 0\) and \(x = d\). The slab contains a non-uniform volume charge density \(\rho(x) = \rho_0 \sin\left(\dfrac{\pi x}{d}\right)\) for \(0 \le x \le d\), where \(\rho_0\) is a positive constant. Which of the following expressions gives the \(x\)-component of the electric field, \(E_x(x)\), inside the slab as a function of position \(x\) for \(0 \le x \le d\)?

![A cross-sectional diagram of a planar slab between x = 0 and x = d in the xy-plane. A horizontal x-axis extends through the slab with tick marks labeled 0, d/2, and d. Vertical dashed lines mark the slab boundaries at x = 0 and x = d. Gray shading inside the slab is darkest at x = d/2 and smoothly fades toward zero at x = 0 and x = d. A vertical dashed line at x = d/2 indicates the symmetry plane. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830563-o6et40.jpg)

- **A.** \(E_x(x) = -\dfrac{\rho_0 d}{\pi \varepsilon_0} \cos\left(\dfrac{\pi x}{d}\right)\)
- **B.** \(E_x(x) = \dfrac{\rho_0 d}{\pi \varepsilon_0} \left(1 - \cos\left(\dfrac{\pi x}{d}\right)\right)\)
- **C.** \(E_x(x) = -\dfrac{\rho_0 d}{\pi \varepsilon_0} \sin\left(\dfrac{\pi x}{d}\right)\)
- **D.** \(E_x(x) = -\dfrac{\rho_0 d}{2\pi \varepsilon_0} \cos\left(\dfrac{\pi x}{d}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117967/*