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title: "A single-turn circular loop of flexible wire lies in the plane of the page in a uniform, constant magnetic field of magnitude \\(B\\) directed into the page. At time \\(t = 0\\), the loop has an initial radius \\(r_0\\) and begins expanding radially outward in the plane such that its radius as a function of time is \\(r(t) = r_0 + v_0 t\\), where \\(v_0\\) is a constant speed. Which of the following expressions correctly gives the magnitude of the instantaneous electromotive force \\(\\varepsilon(t)\\) induced in the loop as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/123260/"
date_modified: "2026-09-28T11:58:02+00:00"
---

# A single-turn circular loop of flexible wire lies in the plane of the page in a uniform, constant magnetic field of magnitude \(B\) directed into the page. At time \(t = 0\), the loop has an initial radius \(r_0\) and begins expanding radially outward in the plane such that its radius as a function of time is \(r(t) = r_0 + v_0 t\), where \(v_0\) is a constant speed. Which of the following expressions correctly gives the magnitude of the instantaneous electromotive force \(\varepsilon(t)\) induced in the loop as a function of time \(t\)?

A single-turn circular loop of flexible wire lies in the plane of the page in a uniform, constant magnetic field of magnitude \(B\) directed into the page. At time \(t = 0\), the loop has an initial radius \(r_0\) and begins expanding radially outward in the plane such that its radius as a function of time is \(r(t) = r_0 + v_0 t\), where \(v_0\) is a constant speed. Which of the following expressions correctly gives the magnitude of the instantaneous electromotive force \(\varepsilon(t)\) induced in the loop as a function of time \(t\)?

![A circular loop of wire is centered in a region of uniform magnetic field directed perpendicularly into the page, represented by a grid of small x symbols. The loop has a dashed inner circle of radius \(r_0\) and a solid outer circle representing the expanded loop of radius \(r(t)\) at time \(t\). Four outward-pointing arrows, each labeled \(v_0\), are attached to the outer circle at the top, bottom, left, and right, indicating uniform radial expansion. A single straight radial line extends from the center to the outer perimeter, labeled \(r(t)\). A field symbol labeled \(\vec{B}\) appears in the upper right. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596682-8Yp1sh.jpg)

- **A.** \(\varepsilon(t) = \pi B v_0 (r_0 + v_0 t)\)
- **B.** \(\varepsilon(t) = 2\pi B v_0 (r_0 + v_0 t)\)
- **C.** \(\varepsilon(t) = \pi B v_0 (2r_0 + v_0 t)\)
- **D.** \(\varepsilon(t) = 2\pi B v_0 (2r_0 + v_0 t)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123260/*