---
title: "In a two-dimensional region of space, a series of concentric circular equipotential curves is mapped. The electric potential of the \\(n\\text{th}\\) curve is given by \\(V_n = n V_0\\), where \\(n = 1, 2, 3, \\dots\\), and its corresponding radius is \\(r_n = R_0 \\sqrt{n}\\), where \\(V_0\\) and \\(R_0\\) are positive constants. Which of the following expressions best represents the magnitude of the radial electric field \\(E(r)\\) as a function of distance \\(r\\) from the origin?"
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url: "https://nerd-notes.com/ubq/118108/"
date_modified: "2026-08-04T08:05:10+00:00"
---

# In a two-dimensional region of space, a series of concentric circular equipotential curves is mapped. The electric potential of the \(n\text{th}\) curve is given by \(V_n = n V_0\), where \(n = 1, 2, 3, \dots\), and its corresponding radius is \(r_n = R_0 \sqrt{n}\), where \(V_0\) and \(R_0\) are positive constants. Which of the following expressions best represents the magnitude of the radial electric field \(E(r)\) as a function of distance \(r\) from the origin?

In a two-dimensional region of space, a series of concentric circular equipotential curves is mapped. The electric potential of the \(n\text{th}\) curve is given by \(V_n = n V_0\), where \(n = 1, 2, 3, \dots\), and its corresponding radius is \(r_n = R_0 \sqrt{n}\), where \(V_0\) and \(R_0\) are positive constants. Which of the following expressions best represents the magnitude of the radial electric field \(E(r)\) as a function of distance \(r\) from the origin?

![A 2D coordinate plot centered at the origin showing three concentric dashed circular lines representing equipotential curves. The innermost circle of radius R_0 is labeled V_0. The second circle of radius \sqrt{2}R_0 is labeled 2V_0. The third circle of radius \sqrt{3}R_0 is labeled 3V_0. The axes are labeled x and y. No other labels, lines, text, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830710-QHClTJ.jpg)

- **A.** \(\dfrac{V_0}{R_0}\)
- **B.** \(\dfrac{V_0 R_0}{r^2}\)
- **C.** \(\dfrac{2 V_0 r}{R_0^2}\)
- **D.** \(\dfrac{V_0 r}{R_0^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118108/*