---
title: "An uncharged solid conducting sphere of radius \\(R\\) is placed in a uniform external electric field \\(\\vec{E}_0 = E_0\\hat{i}\\), reaching electrostatic equilibrium. Four locations are identified: point \\(P\\) at the center of the sphere, point \\(Q\\) immediately outside the sphere at \\((R^+, 0)\\), point \\(S\\) immediately outside the sphere at \\((0, R^+)\\), and point \\(T\\) immediately outside the sphere at \\((R\\cos 45^\\circ, R\\sin 45^\\circ)\\). Which of the following diagrams correctly represents the directions and relative magnitudes of the net electric field vectors at points \\(P\\), \\(Q\\), \\(S\\), and \\(T\\)?"
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url: "https://nerd-notes.com/ubq/124753/"
date_modified: "2026-09-28T14:09:59+00:00"
---

# An uncharged solid conducting sphere of radius \(R\) is placed in a uniform external electric field \(\vec{E}_0 = E_0\hat{i}\), reaching electrostatic equilibrium. Four locations are identified: point \(P\) at the center of the sphere, point \(Q\) immediately outside the sphere at \((R^+, 0)\), point \(S\) immediately outside the sphere at \((0, R^+)\), and point \(T\) immediately outside the sphere at \((R\cos 45^\circ, R\sin 45^\circ)\). Which of the following diagrams correctly represents the directions and relative magnitudes of the net electric field vectors at points \(P\), \(Q\), \(S\), and \(T\)?

An uncharged solid conducting sphere of radius \(R\) is placed in a uniform external electric field \(\vec{E}_0 = E_0\hat{i}\), reaching electrostatic equilibrium. Four locations are identified: point \(P\) at the center of the sphere, point \(Q\) immediately outside the sphere at \((R^+, 0)\), point \(S\) immediately outside the sphere at \((0, R^+)\), and point \(T\) immediately outside the sphere at \((R\cos 45^\circ, R\sin 45^\circ)\). Which of the following diagrams correctly represents the directions and relative magnitudes of the net electric field vectors at points \(P\), \(Q\), \(S\), and \(T\)?

![A circle of radius \(R\) with a light gray solid fill is centered at the origin of a two-dimensional Cartesian plane with a horizontal axis labeled \(x\) and a vertical axis labeled \(y\). Three horizontal dashed arrows of equal length point toward the right, evenly spaced vertically above, through, and below the circle, with the topmost arrow labeled \(\vec{E}_0\). Four distinct points are marked with small solid black dots: point \(P\) at the origin \((0,0)\), point \(Q\) on the positive \(x\)-axis immediately outside the circle at \((R,0)\), point \(S\) on the positive \(y\)-axis immediately outside the circle at \((0,R)\), and point \(T\) immediately outside the circle in the first quadrant along a line making a \(45^\circ\) angle with the positive \(x\)-axis. A dashed radial line extends from the origin through point \(T\), with an arc between the positive \(x\)-axis and the dashed line labeled \(45^\circ\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-diag-1-1790604597-F1aYHk.jpg)

- **A.** Diagram A
- **B.** Diagram B
- **C.** Diagram C
- **D.** Diagram D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124753/*