---
title: "A spherical conducting liquid droplet of radius \\(R\\) carries a total charge \\(Q\\). The droplet splits into two identical, smaller spherical droplets that separate until they are infinitely far apart. What is the ratio \\(U_f / U_i\\) of the total electrostatic potential energy of the two-droplet system when far apart to the initial electrostatic potential energy of the single droplet?"
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url: "https://nerd-notes.com/ubq/118168/"
date_modified: "2026-08-04T08:05:37+00:00"
---

# A spherical conducting liquid droplet of radius \(R\) carries a total charge \(Q\). The droplet splits into two identical, smaller spherical droplets that separate until they are infinitely far apart. What is the ratio \(U_f / U_i\) of the total electrostatic potential energy of the two-droplet system when far apart to the initial electrostatic potential energy of the single droplet?

A spherical conducting liquid droplet of radius \(R\) carries a total charge \(Q\). The droplet splits into two identical, smaller spherical droplets that separate until they are infinitely far apart. What is the ratio \(U_f / U_i\) of the total electrostatic potential energy of the two-droplet system when far apart to the initial electrostatic potential energy of the single droplet?

![A two-panel schematic diagram aligned horizontally. On the left, labeled Initial, a single shaded circle of radius R is centered, labeled with charge Q. A rightward arrow labeled Split points from the left panel to the right panel. On the right, labeled Final, two smaller identical shaded circles, each of radius r, are shown separated horizontally by a large distance, each labeled with charge q = Q/2. No other labels, lines, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830737-FUg7qZ.jpg)

- **A.** \(2^{-1}\)
- **B.** \(2^{-2/3}\)
- **C.** \(2^{-1/3}\)
- **D.** \(2^{1/3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118168/*