---
title: "A thin, nonconducting spherical shell of radius \\(R\\) carries a uniform positive charge \\(+Q\\). A small hole is drilled through the shell wall. A point particle of mass \\(m\\) and negative charge \\(-q\\) (where \\(q > 0\\)) is released from rest at a radial distance \\(r = 3R\\) from the center of the shell. Assuming gravitational effects and the hole’s effect on the electric field are negligible, what is the speed of the particle as it passes through the center of the shell?"
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url: "https://nerd-notes.com/ubq/118166/"
date_modified: "2026-08-04T08:05:37+00:00"
---

# A thin, nonconducting spherical shell of radius \(R\) carries a uniform positive charge \(+Q\). A small hole is drilled through the shell wall. A point particle of mass \(m\) and negative charge \(-q\) (where \(q > 0\)) is released from rest at a radial distance \(r = 3R\) from the center of the shell. Assuming gravitational effects and the hole’s effect on the electric field are negligible, what is the speed of the particle as it passes through the center of the shell?

A thin, nonconducting spherical shell of radius \(R\) carries a uniform positive charge \(+Q\). A small hole is drilled through the shell wall. A point particle of mass \(m\) and negative charge \(-q\) (where \(q > 0\)) is released from rest at a radial distance \(r = 3R\) from the center of the shell. Assuming gravitational effects and the hole's effect on the electric field are negligible, what is the speed of the particle as it passes through the center of the shell?

![A thin spherical shell of radius R centered at the origin, with positive signs evenly spaced along its perimeter. A small opening is shown on the right side of the shell along the horizontal axis. A point particle labeled -q with mass m is located on the horizontal axis at distance 3R to the right of the center. A dashed line along the horizontal axis extends from the particle through the hole to the center of the shell. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830736-I5q1A2.jpg)

- **A.** \( \sqrt{\dfrac{q Q}{6\pi\varepsilon_0 m R}} \)
- **B.** \( \sqrt{\dfrac{q Q}{2\pi\varepsilon_0 m R}} \)
- **C.** \( \sqrt{\dfrac{2q Q}{3\pi\varepsilon_0 m R}} \)
- **D.** \( \sqrt{\dfrac{q Q}{3\pi\varepsilon_0 m R}} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118166/*