---
title: "A spherical shell resistor is constructed from a material of uniform resistivity \\(\\rho\\) bounded by inner radius \\(a\\) and outer radius \\(b\\). Thin conducting concentric shells at \\(r = a\\) and \\(r = b\\) are connected to a potential difference such that a steady total current \\(I\\) flows radially outward through the resistive material. Which of the following expressions correctly gives the total electrical resistance \\(R\\) of the spherical shell and the magnitude of the radial electric field \\(E(r)\\) at a distance \\(r\\) from the center, where \\(a < r < b\\)?"
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/118433/"
date_modified: "2026-08-04T08:10:03+00:00"
---

# A spherical shell resistor is constructed from a material of uniform resistivity \(\rho\) bounded by inner radius \(a\) and outer radius \(b\). Thin conducting concentric shells at \(r = a\) and \(r = b\) are connected to a potential difference such that a steady total current \(I\) flows radially outward through the resistive material. Which of the following expressions correctly gives the total electrical resistance \(R\) of the spherical shell and the magnitude of the radial electric field \(E(r)\) at a distance \(r\) from the center, where \(a < r < b\)?

A spherical shell resistor is constructed from a material of uniform resistivity \(\rho\) bounded by inner radius \(a\) and outer radius \(b\). Thin conducting concentric shells at \(r = a\) and \(r = b\) are connected to a potential difference such that a steady total current \(I\) flows radially outward through the resistive material. Which of the following expressions correctly gives the total electrical resistance \(R\) of the spherical shell and the magnitude of the radial electric field \(E(r)\) at a distance \(r\) from the center, where \(a < r < b\)?

![A cross-sectional view of a spherical shell resistor centered at the origin. Two concentric circular boundaries represent thin conducting shells: an inner circle of radius a and an outer circle of radius b, with a > 0 and b > a. The region between r = a and r = b is shaded light gray to represent the resistive material of resistivity \rho. A dashed line with a single arrowhead extends from the center to the inner boundary, labeled a. Another dashed line with a single arrowhead extends from the center to the outer boundary, labeled b. Four straight arrows, evenly spaced at 90-degree angles around the circle, point radially outward from the inner shell at r = a to the outer shell at r = b, each labeled with the letter I to indicate current flow. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831003-H14JFL.jpg)

- **A.** \(R = \dfrac{\rho \ln(b/a)}{2\pi(b-a)}\), \quad \(E(r) = \dfrac{\rho I}{2\pi r(b-a)}\)
- **B.** \(R = \dfrac{\rho(b-a)}{4\pi a b}\), \quad \(E(r) = \dfrac{\rho I}{4\pi r(b-a)}\)
- **C.** \(R = \dfrac{\rho(b-a)}{4\pi a b}\), \quad \(E(r) = \dfrac{\rho I}{4\pi r^2}\)
- **D.** \(R = \dfrac{\rho(b^2-a^2)}{4\pi a b^2}\), \quad \(E(r) = \dfrac{\rho I}{4\pi r^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118433/*