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title: "An ideal LC circuit consists of an air-filled parallel-plate capacitor with plate area \\(A\\) and plate separation \\(d\\), connected to an ideal long solenoid inductor of length \\(\\ell\\), cross-sectional area \\(A_s\\), and \\(N\\) total turns. The capacitor is initially charged to a potential difference \\(V_0\\) and then connected across the solenoid at time \\(t = 0\\). In terms of \\(V_0\\), \\(A\\), \\(d\\), \\(A_s\\), \\(\\ell\\), and physical constants, what is the maximum magnitude \\(B_{\\text{max}}\\)"
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url: "https://nerd-notes.com/ubq/118732/"
date_modified: "2026-08-04T08:13:58+00:00"
---

# An ideal LC circuit consists of an air-filled parallel-plate capacitor with plate area \(A\) and plate separation \(d\), connected to an ideal long solenoid inductor of length \(\ell\), cross-sectional area \(A_s\), and \(N\) total turns. The capacitor is initially charged to a potential difference \(V_0\) and then connected across the solenoid at time \(t = 0\). In terms of \(V_0\), \(A\), \(d\), \(A_s\), \(\ell\), and physical constants, what is the maximum magnitude \(B_{\text{max}}\)

An ideal LC circuit consists of an air-filled parallel-plate capacitor with plate area \(A\) and plate separation \(d\), connected to an ideal long solenoid inductor of length \(\ell\), cross-sectional area \(A_s\), and \(N\) total turns. The capacitor is initially charged to a potential difference \(V_0\) and then connected across the solenoid at time \(t = 0\). In terms of \(V_0\), \(A\), \(d\), \(A_s\), \(\ell\), and physical constants, what is the maximum magnitude \(B_{\text{max}}\)

![A simple schematic diagram of an LC circuit drawn as a single rectangular loop. On the left vertical branch sits a parallel-plate capacitor shown as two equal horizontal parallel plate segments separated by a gap labeled d, with plate area labeled A. On the right vertical branch sits an ideal long solenoid drawn as a series of six tight helical loops of length \ell, cross-sectional area A_s, and N turns. Connecting wire lines complete the top and bottom paths. An open switch S is located on the top horizontal wire segment. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831238-IgkPeA.jpg)

- **A.** \(V_0 \sqrt{\dfrac{\mu_0 \varepsilon_0 d}{A A_s \ell}}\)
- **B.** \(V_0 \sqrt{\dfrac{\mu_0 \varepsilon_0 A_s}{d A \ell}}\)
- **C.** \(V_0 \sqrt{\dfrac{\mu_0 \varepsilon_0 A d}{A_s \ell^3}}\)
- **D.** \(V_0 \sqrt{\dfrac{\mu_0 \varepsilon_0 A}{d A_s \ell}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118732/*