---
title: "An ideal solenoid of length \\(\\ell\\) and cross-sectional area \\(A\\) consists of \\(N\\) tightly wound turns of wire. When the number of turns is doubled to \\(2N\\) while keeping both \\(\\ell\\) and \\(A\\) constant, the self-inductance of the solenoid quadruples. Which of the following best explains why the self-inductance quadruples rather than doubles?"
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url: "https://nerd-notes.com/ubq/118715/"
date_modified: "2026-08-11T10:54:57+00:00"
---

# An ideal solenoid of length \(\ell\) and cross-sectional area \(A\) consists of \(N\) tightly wound turns of wire. When the number of turns is doubled to \(2N\) while keeping both \(\ell\) and \(A\) constant, the self-inductance of the solenoid quadruples. Which of the following best explains why the self-inductance quadruples rather than doubles?

An ideal solenoid of length \(\ell\) and cross-sectional area \(A\) consists of \(N\) tightly wound turns of wire. When the number of turns is doubled to \(2N\) while keeping both \(\ell\) and \(A\) constant, the self-inductance of the solenoid quadruples. Which of the following best explains why the self-inductance quadruples rather than doubles?

![A horizontal cylindrical solenoid of length \(\ell\) and circular cross-sectional area \(A\) wound evenly with \(N\) turns of wire carrying a current \(I\). A central longitudinal axis runs horizontally through the center of the cylinder. A rightward arrow along the axis is labeled with the magnetic field vector \(\vec{B}\). Dimension lines indicate the overall length \(\ell\) of the solenoid and the cross-sectional area \(A\) at one circular end. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/ubq-frq-generatedstem-fig-1-1786445697-uCD3Ka.jpg)

- **A.** Doubling the number of turns quadruples the magnetic field magnitude inside the solenoid for a given current, which quadruples the magnetic flux passing through each individual turn.
- **B.** Doubling the number of turns doubles the total magnetic flux through a single turn, but the self-inductance depends only on the wire length rather than the number of turns linking the flux.
- **C.** Doubling the number of turns doubles the magnetic field magnitude per unit current, thereby doubling the flux through each turn, while also doubling the number of turns that link this flux.
- **D.** Doubling the number of turns doubles the magnetic field magnitude inside the solenoid, which quadruples the total volume occupied by the magnetic field without altering the flux per turn.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118715/*