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title: "Two identical conducting spheres of radius \\(R\\) are separated by a center-to-center distance \\(d \\gg R\\). Initially, one sphere carries a net charge \\(Q_0\\) and the other sphere is neutral, giving the two-sphere system an initial total electrostatic potential energy \\(U_0\\). A thin wire of negligible electrical resistance connects the two spheres, allowing charge to transfer until a new electrostatic equilibrium is reached, resulting in a final total electrostatic potential energy of \\(\\dfrac{1}{2}U_0\\). Which of the following statements best explains why the final electrostatic potential energy is less than the initial electrostatic potential energy?"
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url: "https://nerd-notes.com/ubq/124495/"
date_modified: "2026-09-28T14:08:19+00:00"
---

# Two identical conducting spheres of radius \(R\) are separated by a center-to-center distance \(d \gg R\). Initially, one sphere carries a net charge \(Q_0\) and the other sphere is neutral, giving the two-sphere system an initial total electrostatic potential energy \(U_0\). A thin wire of negligible electrical resistance connects the two spheres, allowing charge to transfer until a new electrostatic equilibrium is reached, resulting in a final total electrostatic potential energy of \(\dfrac{1}{2}U_0\). Which of the following statements best explains why the final electrostatic potential energy is less than the initial electrostatic potential energy?

Two identical conducting spheres of radius \(R\) are separated by a center-to-center distance \(d \gg R\). Initially, one sphere carries a net charge \(Q_0\) and the other sphere is neutral, giving the two-sphere system an initial total electrostatic potential energy \(U_0\). A thin wire of negligible electrical resistance connects the two spheres, allowing charge to transfer until a new electrostatic equilibrium is reached, resulting in a final total electrostatic potential energy of \(\dfrac{1}{2}U_0\). Which of the following statements best explains why the final electrostatic potential energy is less than the initial electrostatic potential energy?

![A schematic showing two identical circles of radius \(R\) positioned along a horizontal axis, separated by center-to-center distance \(d\). The left circle is shaded light gray and labeled \(Q_0\) at its center. A radial dashed line segment extends from the center of the left circle to its boundary, labeled \(R\). The right circle is unshaded with a solid black outline and labeled neutral. A thin horizontal line connects the highest point of the left circle to the highest point of the right circle. A horizontal dimension line with two arrowheads sits below both circles, indicating the center-to-center separation distance labeled \(d\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604499-AptcVS.jpg)

- **A.** The reduction in potential energy corresponds to the work required to eliminate the initial electric field within the conducting material of the charged sphere so that the interior electrostatic field becomes zero at equilibrium.
- **B.** Because the wire has negligible resistance, the process is completely conservative, meaning the missing energy remains stored in the persistent magnetic field established around the wire during the charge redistribution.
- **C.** The lost electrostatic energy is converted into mutual interaction energy between the spheres, whose like charges produce a negative mutual potential energy that exactly cancels half of the self-energy.
- **D.** The initial potential difference accelerates the mobile charges, converting electrostatic potential energy into kinetic energy that is dissipated as electromagnetic radiation and microscopic scattering as the system settles into a static state.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124495/*