---
title: "A thin, nonconducting disk of radius \\(R\\) lies in the \\(xy\\)-plane centered at the origin and carries a total charge \\(Q\\) distributed uniformly over its surface. The magnitude of the electric field along the \\(z\\)-axis for \\(z > 0\\) is given by  \\[ E(z) = \\dfrac{Q}{2\\pi\\varepsilon_0 R^2}\\left(1 – \\dfrac{z}{\\sqrt{z^2 + R^2}}\\right) \\]  Which of the following expressions correctly describes the asymptotic behavior of \\(E(z)\\) in the limit \\(z \\gg R\\), and what physical interpretation does it support?"
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url: "https://nerd-notes.com/ubq/117972/"
date_modified: "2026-08-04T08:02:44+00:00"
---

# A thin, nonconducting disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a total charge \(Q\) distributed uniformly over its surface. The magnitude of the electric field along the \(z\)-axis for \(z > 0\) is given by

\[ E(z) = \dfrac{Q}{2\pi\varepsilon_0 R^2}\left(1 – \dfrac{z}{\sqrt{z^2 + R^2}}\right) \]

Which of the following expressions correctly describes the asymptotic behavior of \(E(z)\) in the limit \(z \gg R\), and what physical interpretation does it support?

A thin, nonconducting disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a total charge \(Q\) distributed uniformly over its surface. The magnitude of the electric field along the \(z\)-axis for \(z > 0\) is given by

\[ E(z) = \dfrac{Q}{2\pi\varepsilon_0 R^2}\left(1 - \dfrac{z}{\sqrt{z^2 + R^2}}\right) \]

Which of the following expressions correctly describes the asymptotic behavior of \(E(z)\) in the limit \(z \gg R\), and what physical interpretation does it support?

![A thin circular disk of radius R centered at the origin in the xy-plane. The disk is shaded light blue to indicate uniform charge Q. A vertical dashed z-axis extends upward through the center of the disk. A point P is marked on the z-axis at height z above the center with a small black dot. A vertical dimension line labeled z extends from the origin to point P. A radial line from the center to the disk edge is labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830564-vEDY1j.jpg)

- **A.** \(E(z) \approx \dfrac{Q}{4\pi\varepsilon_0 z^2}\), indicating that at large distances the disk behaves as a point charge of charge \(Q\).
- **B.** \(E(z) \approx \dfrac{Q}{2\pi\varepsilon_0 R^2}\), indicating that at large distances the electric field approaches a constant uniform value.
- **C.** \(E(z) \approx \dfrac{Q}{2\pi\varepsilon_0 R z}\), indicating that at large distances the field decays inversely with distance, similar to an infinitely long line of charge.
- **D.** \(E(z) \approx \dfrac{QR}{4\pi\varepsilon_0 z^3}\), indicating that at large distances the disk acts as an electric dipole.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117972/*