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title: "A non-linear dielectric material placed between parallel conducting plates has an electric displacement field magnitude given by \\(D = \\varepsilon_0 E + \\beta E^2\\), where \\(E\\) is the electric field magnitude and \\(\\beta\\) is a positive constant. The electrostatic energy density stored in the material is defined by the work required per unit volume to establish the field, given by \\(u = \\int_0^E E’ \\, dD’\\). Which of the following expressions represents the electrostatic energy density \\(u\\) stored in the dielectric?"
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url: "https://nerd-notes.com/ubq/118239/"
date_modified: "2026-08-04T08:08:22+00:00"
---

# A non-linear dielectric material placed between parallel conducting plates has an electric displacement field magnitude given by \(D = \varepsilon_0 E + \beta E^2\), where \(E\) is the electric field magnitude and \(\beta\) is a positive constant. The electrostatic energy density stored in the material is defined by the work required per unit volume to establish the field, given by \(u = \int_0^E E’ \, dD’\). Which of the following expressions represents the electrostatic energy density \(u\) stored in the dielectric?

A non-linear dielectric material placed between parallel conducting plates has an electric displacement field magnitude given by \(D = \varepsilon_0 E + \beta E^2\), where \(E\) is the electric field magnitude and \(\beta\) is a positive constant. The electrostatic energy density stored in the material is defined by the work required per unit volume to establish the field, given by \(u = \int_0^E E' \, dD'\). Which of the following expressions represents the electrostatic energy density \(u\) stored in the dielectric?

- **A.** \(\dfrac{1}{2}\varepsilon_0 E^2 + \dfrac{1}{3}\beta E^3\)
- **B.** \(\dfrac{1}{2}\varepsilon_0 E^2 + \dfrac{1}{2}\beta E^3\)
- **C.** \(\dfrac{1}{2}\varepsilon_0 E^2 + \dfrac{2}{3}\beta E^3\)
- **D.** \(\dfrac{1}{2}\varepsilon_0 E^2 + \beta E^3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118239/*