---
title: "A long, ideal solenoid of radius \\(R\\) has \\(n\\) turns per unit length and carries a time-dependent current given by \\(I(t) = I_0 \\left(1 – \\dfrac{t^2}{T^2}\\right)\\) for \\(0 \\le t \\le T\\), where \\(I_0\\) and \\(T\\) are positive constants. Which of the following expressions gives the magnitude of the induced electric field \\(E(r, t)\\) at a radial distance \\(r > R\\) from the central axis of the solenoid as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/118721/"
date_modified: "2026-08-04T08:13:53+00:00"
---

# A long, ideal solenoid of radius \(R\) has \(n\) turns per unit length and carries a time-dependent current given by \(I(t) = I_0 \left(1 – \dfrac{t^2}{T^2}\right)\) for \(0 \le t \le T\), where \(I_0\) and \(T\) are positive constants. Which of the following expressions gives the magnitude of the induced electric field \(E(r, t)\) at a radial distance \(r > R\) from the central axis of the solenoid as a function of time \(t\)?

A long, ideal solenoid of radius \(R\) has \(n\) turns per unit length and carries a time-dependent current given by \(I(t) = I_0 \left(1 - \dfrac{t^2}{T^2}\right)\) for \(0 \le t \le T\), where \(I_0\) and \(T\) are positive constants. Which of the following expressions gives the magnitude of the induced electric field \(E(r, t)\) at a radial distance \(r > R\) from the central axis of the solenoid as a function of time \(t\)?

![A cross-sectional view of a long cylindrical solenoid of radius R. A dashed circular path of radius r is drawn concentrically outside the solenoid, where r is greater than R. Inside the solenoid circle of radius R, uniform cross symbols represent a magnetic field B directed into the page. A radial line from the center to the solenoid boundary is labeled R, and a radial line from the center to the dashed outer path is labeled r. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831233-DQvR9S.jpg)

- **A.** \(\dfrac{\mu_0 n I_0 r t}{T^2}\)
- **B.** \(\dfrac{2 \mu_0 n I_0 R^2 t}{r T^2}\)
- **C.** \(\dfrac{\mu_0 n I_0 R^2 t}{r T^2}\)
- **D.** \(\dfrac{\mu_0 n I_0 R^2}{r T} \left(1 - \dfrac{t^2}{T^2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118721/*