---
title: "A hollow, open-ended truncated cone has a uniform surface charge density \\(\\sigma\\). The cone has a half-angle \\(\\theta_0\\) and extends along its sloped surface from a slant distance \\(r_1\\) to a slant distance \\(r_2\\) from its apex, as shown in the diagram. Which of the following expressions represents the magnitude of the electric field at the apex of the truncated cone?"
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url: "https://nerd-notes.com/ubq/118014/"
date_modified: "2026-08-04T08:02:55+00:00"
---

# A hollow, open-ended truncated cone has a uniform surface charge density \(\sigma\). The cone has a half-angle \(\theta_0\) and extends along its sloped surface from a slant distance \(r_1\) to a slant distance \(r_2\) from its apex, as shown in the diagram. Which of the following expressions represents the magnitude of the electric field at the apex of the truncated cone?

A hollow, open-ended truncated cone has a uniform surface charge density \(\sigma\). The cone has a half-angle \(\theta_0\) and extends along its sloped surface from a slant distance \(r_1\) to a slant distance \(r_2\) from its apex, as shown in the diagram. Which of the following expressions represents the magnitude of the electric field at the apex of the truncated cone?

![A 3D perspective diagram showing a hollow truncated cone aligned symmetrically along the positive z-axis, with its imaginary apex located at the origin O. The half-angle at the apex is labeled \theta_0, measured between the central z-axis and the sloped side of the cone. The inner boundary of the truncated cone is a circle at slant distance r_1 from the origin O, and the outer boundary is a larger circle at slant distance r_2 from the origin O. The sloped surface between r_1 and r_2 is shaded lightly and labeled with uniform surface charge density \sigma. The point at the origin is labeled 'Apex'. No other vectors, field lines, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830575-ELa0RG.jpg)

- **A.** \(\dfrac{\sigma \sin\theta_0}{2\varepsilon_0} \ln\left(\dfrac{r_2}{r_1}\right)\)
- **B.** \(\dfrac{\sigma \sin\theta_0 \cos\theta_0}{2\varepsilon_0} \ln\left(\dfrac{r_2}{r_1}\right)\)
- **C.** \(\dfrac{\sigma \sin\theta_0 \cos^2\theta_0}{2\varepsilon_0} \ln\left(\dfrac{r_2}{r_1}\right)\)
- **D.** \(\dfrac{\sigma \sin\theta_0 \cos\theta_0}{\varepsilon_0} \ln\left(\dfrac{r_2}{r_1}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118014/*