---
title: "A thin wire carrying a total charge \\(Q\\) is wound into a flat, tightly packed spiral with inner radius \\(a\\) and outer radius \\(b\\). The winding turns are spaced uniformly so that the charge can be modeled as a continuous surface charge distribution with uniform surface charge density \\(\\sigma\\) over the region \\(a \\le r \\le b\\). Which of the following expressions correctly gives the electric potential at the center of the spiral relative to infinity?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118117/"
date_modified: "2026-08-04T08:05:13+00:00"
---

# A thin wire carrying a total charge \(Q\) is wound into a flat, tightly packed spiral with inner radius \(a\) and outer radius \(b\). The winding turns are spaced uniformly so that the charge can be modeled as a continuous surface charge distribution with uniform surface charge density \(\sigma\) over the region \(a \le r \le b\). Which of the following expressions correctly gives the electric potential at the center of the spiral relative to infinity?

A thin wire carrying a total charge \(Q\) is wound into a flat, tightly packed spiral with inner radius \(a\) and outer radius \(b\). The winding turns are spaced uniformly so that the charge can be modeled as a continuous surface charge distribution with uniform surface charge density \(\sigma\) over the region \(a \le r \le b\). Which of the following expressions correctly gives the electric potential at the center of the spiral relative to infinity?

![A flat spiral disk lying in the xy-plane centered at the origin, with inner radius a and outer radius b. The region between r = a and r = b is filled with closely spaced concentric circular turns of a thin wire. A dashed line extends from the origin out to the inner edge at radius a, labeled a. Another dashed line extends from the origin to the outer edge at radius b, labeled b. A point at the origin is labeled O. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830713-doK7CS.jpg)

- **A.** \(\dfrac{Q \ln(b/a)}{4\pi\varepsilon_0(b-a)}\)
- **B.** \(\dfrac{Q}{4\pi\varepsilon_0(b-a)}\)
- **C.** \(\dfrac{Q \ln(b/a)}{2\pi\varepsilon_0(b^2-a^2)}\)
- **D.** \(\dfrac{Q}{2\pi\varepsilon_0(a+b)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118117/*