---
title: "A cylindrical capacitor of length \\(L\\) consists of a solid conducting inner cylinder of radius \\(a\\) and a thin conducting outer cylindrical shell of radius \\(c\\). The space between the conductors is filled with two coaxial cylindrical layers of dielectric materials: the inner layer from radius \\(a\\) to radius \\(b\\) has dielectric constant \\(\\kappa_1\\), and the outer layer from radius \\(b\\) to radius \\(c\\) has dielectric constant \\(\\kappa_2\\). Assuming edge effects are negligible (\\(L \\gg c\\)), which of the following expressions represents the capacitance of this capacitor?"
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url: "https://nerd-notes.com/ubq/118254/"
date_modified: "2026-08-04T08:08:26+00:00"
---

# A cylindrical capacitor of length \(L\) consists of a solid conducting inner cylinder of radius \(a\) and a thin conducting outer cylindrical shell of radius \(c\). The space between the conductors is filled with two coaxial cylindrical layers of dielectric materials: the inner layer from radius \(a\) to radius \(b\) has dielectric constant \(\kappa_1\), and the outer layer from radius \(b\) to radius \(c\) has dielectric constant \(\kappa_2\). Assuming edge effects are negligible (\(L \gg c\)), which of the following expressions represents the capacitance of this capacitor?

A cylindrical capacitor of length \(L\) consists of a solid conducting inner cylinder of radius \(a\) and a thin conducting outer cylindrical shell of radius \(c\). The space between the conductors is filled with two coaxial cylindrical layers of dielectric materials: the inner layer from radius \(a\) to radius \(b\) has dielectric constant \(\kappa_1\), and the outer layer from radius \(b\) to radius \(c\) has dielectric constant \(\kappa_2\). Assuming edge effects are negligible (\(L \gg c\)), which of the following expressions represents the capacitance of this capacitor?

![Cross-sectional diagram of a cylindrical capacitor centered at the origin. A innermost solid circle of radius \(a\) represents the inner conductor. A concentric circle of radius \(b\) marks the boundary between two dielectric regions. An outermost concentric circle of radius \(c\) represents the outer conductor. The region between radius \(a\) and radius \(b\) is shaded light gray and labeled with dielectric constant \(\kappa_1\). The region between radius \(b\) and radius \(c\) is shaded medium gray and labeled with dielectric constant \(\kappa_2\). Three radial line segments extend from the center to each boundary, labeled with radii \(a\), \(b\), and \(c\) respectively. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830906-xMVVA5.jpg)

- **A.** \(C = \dfrac{2\pi \varepsilon_0 L (\kappa_1 + \kappa_2)}{\ln\left(\dfrac{c}{a}\right)}\)
- **B.** \(C = \dfrac{2\pi \varepsilon_0 L}{\kappa_1 \ln\left(\dfrac{b}{a}\right) + \kappa_2 \ln\left(\dfrac{c}{b}\right)}\)
- **C.** \(C = \dfrac{2\pi \varepsilon_0 L \kappa_1 \kappa_2}{\ln\left(\dfrac{b}{a}\right) \ln\left(\dfrac{c}{b}\right)}\)
- **D.** \(C = \dfrac{2\pi \varepsilon_0 L}{\dfrac{1}{\kappa_1} \ln\left(\dfrac{b}{a}\right) + \dfrac{1}{\kappa_2} \ln\left(\dfrac{c}{b}\right)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118254/*