---
title: "A cylindrical region of space with radius \\(R\\) contains a spatially uniform magnetic field directed parallel to the cylinder’s central axis. The magnitude of the magnetic field increases at a constant rate \\(\\dfrac{dB}{dt} = \\alpha\\), and the magnetic field is zero everywhere outside the cylinder (\\(r > R\\)). Which of the following graphs best represents the magnitude of the induced electric field \\(E\\) as a function of radial distance \\(r\\) from the central axis?"
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url: "https://nerd-notes.com/ubq/121366/"
date_modified: "2026-08-23T05:00:01+00:00"
---

# A cylindrical region of space with radius \(R\) contains a spatially uniform magnetic field directed parallel to the cylinder’s central axis. The magnitude of the magnetic field increases at a constant rate \(\dfrac{dB}{dt} = \alpha\), and the magnetic field is zero everywhere outside the cylinder (\(r > R\)). Which of the following graphs best represents the magnitude of the induced electric field \(E\) as a function of radial distance \(r\) from the central axis?

A cylindrical region of space with radius \(R\) contains a spatially uniform magnetic field directed parallel to the cylinder's central axis. The magnitude of the magnetic field increases at a constant rate \(\dfrac{dB}{dt} = \alpha\), and the magnetic field is zero everywhere outside the cylinder (\(r > R\)). Which of the following graphs best represents the magnitude of the induced electric field \(E\) as a function of radial distance \(r\) from the central axis?

![A circular cross section of radius \(R\) centered at a central axis point. The interior of the circle is filled with a grid of small \(\times\) symbols representing a uniform magnetic field \(\vec{B}\) directed into the page. A solid radial line extends from the center to the outer boundary of the circle, labeled \(R\). Outside the circle, the space is empty with no field symbols. Two concentric dashed circular paths are shown: one inside the boundary with a radial arrow from the center labeled \(r < R\), and one outside the boundary with a radial arrow from the center labeled \(r > R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461200-koFsHI.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121366/*