---
title: "An uncharged, solid conducting sphere of radius \\(R\\) is placed near a positive point charge \\(+q\\). The point charge is fixed at a distance \\(d\\) (where \\(d > R\\)) from the center of the sphere, as shown. Which of the following correctly pairs the magnitude of the total electric field at the center of the sphere, \\(E_{\\text{total}}\\), and the magnitude of the electric field at the center of the sphere created solely by the induced charges on the surface, \\(E_{\\text{induced}}\\)?"
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url: "https://nerd-notes.com/ubq/118234/"
date_modified: "2026-08-04T08:08:20+00:00"
---

# An uncharged, solid conducting sphere of radius \(R\) is placed near a positive point charge \(+q\). The point charge is fixed at a distance \(d\) (where \(d > R\)) from the center of the sphere, as shown. Which of the following correctly pairs the magnitude of the total electric field at the center of the sphere, \(E_{\text{total}}\), and the magnitude of the electric field at the center of the sphere created solely by the induced charges on the surface, \(E_{\text{induced}}\)?

An uncharged, solid conducting sphere of radius \(R\) is placed near a positive point charge \(+q\). The point charge is fixed at a distance \(d\) (where \(d > R\)) from the center of the sphere, as shown. Which of the following correctly pairs the magnitude of the total electric field at the center of the sphere, \(E_{\text{total}}\), and the magnitude of the electric field at the center of the sphere created solely by the induced charges on the surface, \(E_{\text{induced}}\)?

![A horizontal dashed line represents the central line of symmetry. On the right, a solid gray circle represents an uncharged conducting sphere of radius R, with its center marked as point C. On the left, a small black circle representing a point charge +q is positioned on the central axis at a distance d from point C. An arrow below the line indicates the distance d between +q and point C, with d > R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830899-J4Scz0.jpg)

- **A.** \(E_{\text{total}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{d^2}\) and \(E_{\text{induced}} = 0\)
- **B.** \(E_{\text{total}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{d^2}\) and \(E_{\text{induced}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{d^2}\)
- **C.** \(E_{\text{total}} = 0\) and \(E_{\text{induced}} = 0\)
- **D.** \(E_{\text{total}} = 0\) and \(E_{\text{induced}} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{d^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118234/*