---
title: "An ideal long cylindrical solenoid with length \\(\\ell\\), circular cross section of radius \\(r\\), and total number of turns \\(N\\) has a self-inductance \\(L\\). A second ideal long cylindrical solenoid is constructed with length \\(2\\ell\\), radius \\(2r\\), and total number of turns \\(2N\\). What is the self-inductance of the second solenoid?"
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url: "https://nerd-notes.com/ubq/118636/"
date_modified: "2026-08-04T08:13:24+00:00"
---

# An ideal long cylindrical solenoid with length \(\ell\), circular cross section of radius \(r\), and total number of turns \(N\) has a self-inductance \(L\). A second ideal long cylindrical solenoid is constructed with length \(2\ell\), radius \(2r\), and total number of turns \(2N\). What is the self-inductance of the second solenoid?

An ideal long cylindrical solenoid with length \(\ell\), circular cross section of radius \(r\), and total number of turns \(N\) has a self-inductance \(L\). A second ideal long cylindrical solenoid is constructed with length \(2\ell\), radius \(2r\), and total number of turns \(2N\). What is the self-inductance of the second solenoid?

- **A.** \(8L\)
- **B.** \(4L\)
- **C.** \(2L\)
- **D.** \(L\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118636/*