---
title: "In a spherically symmetric region of space, the electric potential as a function of radial distance \\(r\\) from the origin is given by \\(V(r) = \\dfrac{V_0 R}{r} e^{-r/R}\\) for \\(r > 0\\), where \\(V_0\\) and \\(R\\) are positive constants. Which of the following expressions represents the magnitude of the radial electric field \\(E(r)\\) in this region?"
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url: "https://nerd-notes.com/ubq/118077/"
date_modified: "2026-08-04T08:05:00+00:00"
---

# In a spherically symmetric region of space, the electric potential as a function of radial distance \(r\) from the origin is given by \(V(r) = \dfrac{V_0 R}{r} e^{-r/R}\) for \(r > 0\), where \(V_0\) and \(R\) are positive constants. Which of the following expressions represents the magnitude of the radial electric field \(E(r)\) in this region?

In a spherically symmetric region of space, the electric potential as a function of radial distance \(r\) from the origin is given by \(V(r) = \dfrac{V_0 R}{r} e^{-r/R}\) for \(r > 0\), where \(V_0\) and \(R\) are positive constants. Which of the following expressions represents the magnitude of the radial electric field \(E(r)\) in this region?

- **A.** \(E(r) = \dfrac{V_0 R}{r^2} \left( 1 + \dfrac{r}{R} \right) e^{-r/R}\)
- **B.** \(E(r) = \dfrac{V_0 R}{r^2} \left( 1 - \dfrac{r}{R} \right) e^{-r/R}\)
- **C.** \(E(r) = \dfrac{V_0 R}{r^2} e^{-r/R}\)
- **D.** \(E(r) = \dfrac{V_0}{r} e^{-r/R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118077/*