---
title: "An ideal \\(LC\\) circuit consists of an inductor of inductance \\(L\\) and a parallel-plate capacitor of capacitance \\(C\\) with horizontal plates of area \\(A\\). At time \\(t = 0\\), the top plate has charge \\(+Q_0\\), the bottom plate has charge \\(-Q_0\\), and the current in the circuit is zero. The angular frequency of oscillation is \\(\\omega = \\dfrac{1}{\\sqrt{LC}}\\), and the maximum magnitude of the electric field between the capacitor plates is \\(E_{\\text{max}} = \\dfrac{Q_0}{A\\varepsilon_0}\\). At time \\(t = \\dfrac{\\pi}{3\\omega}\\), which of the following correctly identifies the magnitude \\(E\\) of the electric field between the plates and whether the magnitude of the field is increasing or decreasing?"
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url: "https://nerd-notes.com/ubq/118709/"
date_modified: "2026-08-04T08:13:49+00:00"
---

# An ideal \(LC\) circuit consists of an inductor of inductance \(L\) and a parallel-plate capacitor of capacitance \(C\) with horizontal plates of area \(A\). At time \(t = 0\), the top plate has charge \(+Q_0\), the bottom plate has charge \(-Q_0\), and the current in the circuit is zero. The angular frequency of oscillation is \(\omega = \dfrac{1}{\sqrt{LC}}\), and the maximum magnitude of the electric field between the capacitor plates is \(E_{\text{max}} = \dfrac{Q_0}{A\varepsilon_0}\). At time \(t = \dfrac{\pi}{3\omega}\), which of the following correctly identifies the magnitude \(E\) of the electric field between the plates and whether the magnitude of the field is increasing or decreasing?

An ideal \(LC\) circuit consists of an inductor of inductance \(L\) and a parallel-plate capacitor of capacitance \(C\) with horizontal plates of area \(A\). At time \(t = 0\), the top plate has charge \(+Q_0\), the bottom plate has charge \(-Q_0\), and the current in the circuit is zero. The angular frequency of oscillation is \(\omega = \dfrac{1}{\sqrt{LC}}\), and the maximum magnitude of the electric field between the capacitor plates is \(E_{\text{max}} = \dfrac{Q_0}{A\varepsilon_0}\). At time \(t = \dfrac{\pi}{3\omega}\), which of the following correctly identifies the magnitude \(E\) of the electric field between the plates and whether the magnitude of the field is increasing or decreasing?

![A single rectangular circuit loop oriented vertically. The left vertical branch contains a parallel-plate capacitor with two horizontal parallel line segments of equal length. The top plate is labeled +Q_0 and the bottom plate is labeled -Q_0. A vertical arrow labeled E_max points downward from the top plate toward the bottom plate between the plates. The right vertical branch contains an inductor drawn as a series of four connected semicircular loops, labeled L. The top horizontal wire connects the top plate of the capacitor to the top of the inductor, and the bottom horizontal wire connects the bottom plate of the capacitor to the bottom of the inductor. No other labels, components, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831229-lBrZOw.jpg)

- **A.** Magnitude: \(\dfrac{\sqrt{3}}{2} E_{\text{max}}\); Behavior: Increasing
- **B.** Magnitude: \(\dfrac{\sqrt{3}}{2} E_{\text{max}}\); Behavior: Decreasing
- **C.** Magnitude: \(\dfrac{1}{2} E_{\text{max}}\); Behavior: Decreasing
- **D.** Magnitude: \(\dfrac{1}{2} E_{\text{max}}\); Behavior: Increasing

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118709/*