---
title: "Two isolated conducting spheres, Sphere 1 of radius \\(R\\) and Sphere 2 of radius \\(2R\\), are located far apart in a vacuum. Sphere 1 initially carries a net charge \\(+Q\\), and Sphere 2 is initially uncharged. At time \\(t = 0\\), the spheres are connected by a thin wire of resistance \\(R_w\\). Which of the following correctly pairs the total charge \\(\\Delta Q\\) transferred from Sphere 1 to Sphere 2 after equilibrium is reached, and the behavior of the current \\(I(t)\\) through the wire as a function of time?"
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url: "https://nerd-notes.com/ubq/118222/"
date_modified: "2026-08-04T08:08:15+00:00"
---

# Two isolated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are located far apart in a vacuum. Sphere 1 initially carries a net charge \(+Q\), and Sphere 2 is initially uncharged. At time \(t = 0\), the spheres are connected by a thin wire of resistance \(R_w\). Which of the following correctly pairs the total charge \(\Delta Q\) transferred from Sphere 1 to Sphere 2 after equilibrium is reached, and the behavior of the current \(I(t)\) through the wire as a function of time?

Two isolated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are located far apart in a vacuum. Sphere 1 initially carries a net charge \(+Q\), and Sphere 2 is initially uncharged. At time \(t = 0\), the spheres are connected by a thin wire of resistance \(R_w\). Which of the following correctly pairs the total charge \(\Delta Q\) transferred from Sphere 1 to Sphere 2 after equilibrium is reached, and the behavior of the current \(I(t)\) through the wire as a function of time?

![Two conducting spheres shown in cross section, separated horizontally. On the left, a smaller sphere of radius \(R\) labeled Sphere 1 with a charge label \(+Q\). On the right, a larger sphere of radius \(2R\) labeled Sphere 2, twice the diameter of Sphere 1, initially uncharged. A thin horizontal line representing a wire connects the top of Sphere 1 to the top of Sphere 2, interrupted by an open switch symbol labeled Switch. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830894-XCUNdS.jpg)

- **A.** Total charge transferred \(\Delta Q = \dfrac{1}{2}Q\) ; Current \(I(t)\) decreases linearly to zero in a finite time
- **B.** Total charge transferred \(\Delta Q = \dfrac{1}{2}Q\) ; Current \(I(t)\) decays exponentially toward zero
- **C.** Total charge transferred \(\Delta Q = \dfrac{2}{3}Q\) ; Current \(I(t)\) remains constant until equilibrium is reached
- **D.** Total charge transferred \(\Delta Q = \dfrac{2}{3}Q\) ; Current \(I(t)\) decays exponentially toward zero

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118222/*