---
title: "An ideal inductor with self-inductance \\(L\\) carries a current that decreases quadratically over the time interval \\(0 \\le t \\le T\\) according to the function \\(I(t) = I_0\\left(1 – \\dfrac{t}{T}\\right)^2\\), where \\(I_0\\) and \\(T\\) are positive constants. At \\(t = 0\\), the magnetic energy stored in the inductor is \\(U_0\\). Which of the following expressions represents the magnitude of the self-induced electromotive force in the inductor at the instant when the stored magnetic energy is equal to \\(\\dfrac{1}{4}U_0\\)?"
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url: "https://nerd-notes.com/ubq/121288/"
date_modified: "2026-08-23T04:59:34+00:00"
---

# An ideal inductor with self-inductance \(L\) carries a current that decreases quadratically over the time interval \(0 \le t \le T\) according to the function \(I(t) = I_0\left(1 – \dfrac{t}{T}\right)^2\), where \(I_0\) and \(T\) are positive constants. At \(t = 0\), the magnetic energy stored in the inductor is \(U_0\). Which of the following expressions represents the magnitude of the self-induced electromotive force in the inductor at the instant when the stored magnetic energy is equal to \(\dfrac{1}{4}U_0\)?

An ideal inductor with self-inductance \(L\) carries a current that decreases quadratically over the time interval \(0 \le t \le T\) according to the function \(I(t) = I_0\left(1 - \dfrac{t}{T}\right)^2\), where \(I_0\) and \(T\) are positive constants. At \(t = 0\), the magnetic energy stored in the inductor is \(U_0\). Which of the following expressions represents the magnitude of the self-induced electromotive force in the inductor at the instant when the stored magnetic energy is equal to \(\dfrac{1}{4}U_0\)?

- **A.** \(\sqrt{2}\dfrac{LI_0}{T}\)
- **B.** \(\dfrac{\sqrt{2}}{2}\dfrac{LI_0}{T}\)
- **C.** \(\dfrac{LI_0}{T}\)
- **D.** 2\dfrac{LI_0}{T}

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121288/*