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title: "A parallel-plate capacitor with vacuum between plates of area \\(A\\) is initially charged to \\(+Q_0\\) and \\(-Q_0\\) on its respective plates at a separation distance \\(d_0\\), storing an initial electrostatic potential energy \\(U_0\\). The capacitor is then disconnected from the charging source, leaving it isolated. An external agent slowly pulls the plates apart until their separation distance is \\(3d_0\\). Assuming edge effects are negligible, which of the following gives the electric field magnitude \\(E\\) between the plates at the new separation and the work \\(W_{\\text{ext}}\\) done by the external agent during the expansion?"
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url: "https://nerd-notes.com/ubq/121140/"
date_modified: "2026-08-23T04:58:17+00:00"
---

# A parallel-plate capacitor with vacuum between plates of area \(A\) is initially charged to \(+Q_0\) and \(-Q_0\) on its respective plates at a separation distance \(d_0\), storing an initial electrostatic potential energy \(U_0\). The capacitor is then disconnected from the charging source, leaving it isolated. An external agent slowly pulls the plates apart until their separation distance is \(3d_0\). Assuming edge effects are negligible, which of the following gives the electric field magnitude \(E\) between the plates at the new separation and the work \(W_{\text{ext}}\) done by the external agent during the expansion?

A parallel-plate capacitor with vacuum between plates of area \(A\) is initially charged to \(+Q_0\) and \(-Q_0\) on its respective plates at a separation distance \(d_0\), storing an initial electrostatic potential energy \(U_0\). The capacitor is then disconnected from the charging source, leaving it isolated. An external agent slowly pulls the plates apart until their separation distance is \(3d_0\). Assuming edge effects are negligible, which of the following gives the electric field magnitude \(E\) between the plates at the new separation and the work \(W_{\text{ext}}\) done by the external agent during the expansion?

![A schematic of a parallel-plate capacitor in vacuum viewed from the side. Two horizontal parallel lines of equal length represent conducting plates of area \(A\). The top plate has a label \(+Q_0\) positioned above its center, and the bottom plate has a label \(-Q_0\) positioned below its center. A vertical double-headed arrow between the inner surfaces of the two plates is labeled \(d_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461096-uPDFUz.jpg)

- **A.** \(E = \dfrac{Q_0}{3\varepsilon_0 A}\) and \(W_{\text{ext}} = \dfrac{2}{3}U_0\)
- **B.** \(E = \dfrac{Q_0}{3\varepsilon_0 A}\) and \(W_{\text{ext}} = 2U_0\)
- **C.** \(E = \dfrac{Q_0}{\varepsilon_0 A}\) and \(W_{\text{ext}} = 2U_0\)
- **D.** \(E = \dfrac{Q_0}{\varepsilon_0 A}\) and \(W_{\text{ext}} = 3U_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121140/*