---
title: "A solid conducting sphere of radius \\(R\\) carries a net positive charge \\(Q\\), resulting in a uniform surface charge density \\(\\sigma\\). Because like charges on the outer surface repel one another, the surface experiences an outward mechanical force per unit area, known as electrostatic pressure \\(P\\). Which of the following expressions represents this electrostatic pressure \\(P\\) in terms of \\(\\sigma\\) and fundamental constants?"
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url: "https://nerd-notes.com/ubq/118252/"
date_modified: "2026-08-04T08:08:26+00:00"
---

# A solid conducting sphere of radius \(R\) carries a net positive charge \(Q\), resulting in a uniform surface charge density \(\sigma\). Because like charges on the outer surface repel one another, the surface experiences an outward mechanical force per unit area, known as electrostatic pressure \(P\). Which of the following expressions represents this electrostatic pressure \(P\) in terms of \(\sigma\) and fundamental constants?

A solid conducting sphere of radius \(R\) carries a net positive charge \(Q\), resulting in a uniform surface charge density \(\sigma\). Because like charges on the outer surface repel one another, the surface experiences an outward mechanical force per unit area, known as electrostatic pressure \(P\). Which of the following expressions represents this electrostatic pressure \(P\) in terms of \(\sigma\) and fundamental constants?

![A circle representing a spherical conductor centered at O with radius arrow labeled R. The outer boundary of the circle is lined with positive sign symbols (+). Small outward radial arrows surround the entire circle to represent electrostatic pressure P. A small patch of area on the top surface is highlighted and labeled dA, with an outward vector arrow labeled dF.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830905-5ArPvg.jpg)

- **A.** \(\dfrac{\sigma^2}{\varepsilon_0}\)
- **B.** \(\dfrac{\sigma^2}{4\varepsilon_0}\)
- **C.** \(\dfrac{\sigma^2}{2\varepsilon_0}\)
- **D.** \(\dfrac{2\sigma^2}{\varepsilon_0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118252/*