---
title: "An isolated solid conducting sphere of radius \\(R\\) carries a net positive charge \\(Q\\) in electrostatic equilibrium.  Due to the mutual repulsion of the surface charge, an outward radial force acts on each surface element, producing an outward electrostatic pressure \\(P\\) across the sphere’s surface.  In terms of \\(Q\\), \\(R\\), and physical constants, which of the following is a correct expression for the electrostatic pressure \\(P\\)?"
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url: "https://nerd-notes.com/ubq/124502/"
date_modified: "2026-09-28T14:08:24+00:00"
---

# An isolated solid conducting sphere of radius \(R\) carries a net positive charge \(Q\) in electrostatic equilibrium.

Due to the mutual repulsion of the surface charge, an outward radial force acts on each surface element, producing an outward electrostatic pressure \(P\) across the sphere’s surface.

In terms of \(Q\), \(R\), and physical constants, which of the following is a correct expression for the electrostatic pressure \(P\)?

An isolated solid conducting sphere of radius \(R\) carries a net positive charge \(Q\) in electrostatic equilibrium.

Due to the mutual repulsion of the surface charge, an outward radial force acts on each surface element, producing an outward electrostatic pressure \(P\) across the sphere's surface.

In terms of \(Q\), \(R\), and physical constants, which of the following is a correct expression for the electrostatic pressure \(P\)?

![A circular boundary centered in the diagram represents the spherical conductor. A small dot marks the geometric center, and a single dashed line segment extends horizontally to the right from the center to the circle's perimeter, labeled with the symbol \(R\) immediately above the midpoint of the segment. Exactly six plus signs are positioned symmetrically around the outer perimeter of the circle. Originating just outside each plus sign, a short solid arrow with an open arrowhead points radially outward away from the center. Outside the upper-right portion of the circle, the charge is labeled \(+Q\). All lines and symbols are rendered in black and grayscale. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604504-YAZYnL.jpg)

- **A.** \(\dfrac{Q^2}{64\pi^2 \varepsilon_0 R^4}\)
- **B.** \(\dfrac{Q^2}{32\pi^2 \varepsilon_0 R^4}\)
- **C.** \(\dfrac{Q^2}{16\pi^2 \varepsilon_0 R^4}\)
- **D.** \(\dfrac{Q^2}{8\pi^2 \varepsilon_0 R^4}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124502/*