---
title: "A long, ideal solenoid of radius \\(R\\) has \\(n\\) turns per unit length. The solenoid carries a time-varying current \\(I(t)\\) that increases at a constant rate \\(\\dfrac{dI}{dt} = C\\), where \\(C > 0\\). Which of the following expressions gives the magnitude of the induced electric field \\(E\\) at a distance \\(r\\) from the central axis of the solenoid, where \\(r < R\\)?"
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url: "https://nerd-notes.com/ubq/118707/"
date_modified: "2026-08-04T08:13:49+00:00"
---

# A long, ideal solenoid of radius \(R\) has \(n\) turns per unit length. The solenoid carries a time-varying current \(I(t)\) that increases at a constant rate \(\dfrac{dI}{dt} = C\), where \(C > 0\). Which of the following expressions gives the magnitude of the induced electric field \(E\) at a distance \(r\) from the central axis of the solenoid, where \(r < R\)?

A long, ideal solenoid of radius \(R\) has \(n\) turns per unit length. The solenoid carries a time-varying current \(I(t)\) that increases at a constant rate \(\dfrac{dI}{dt} = C\), where \(C > 0\). Which of the following expressions gives the magnitude of the induced electric field \(E\) at a distance \(r\) from the central axis of the solenoid, where \(r < R\)?

![A cross-sectional view of a long cylindrical solenoid. A large solid circle represents the outer boundary of radius R, centered at a central point. A straight solid arrow extends from the central point to the outer circle boundary, labeled R. Concentric within the outer circle is a smaller dashed circle representing a path of radius r. A straight solid arrow extends from the central point to the dashed circle, labeled r. Four small curved arrows lie along the dashed circle, pointing in the counterclockwise direction, labeled E. Four small dots distributed evenly inside the outer circle represent a magnetic field directed out of the page. No other lines, labels, text, or visual elements are present.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/solenoid-cross-section-1785831229-OyPJ2h.jpg)

- **A.** \(E = \mu_0 n C r\)
- **B.** \(E = \dfrac{\mu_0 n C R^2}{2r}\)
- **C.** \(E = \dfrac{1}{2} \mu_0 n C r\)
- **D.** \(E = \dfrac{\mu_0 n C r}{2\pi}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118707/*