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title: "A long cylindrical capacitor of length \\(L\\) consists of a solid inner conducting cylinder of radius \\(a\\) and a thin coaxial outer conducting cylindrical shell of radius \\(b\\), where \\(L \\gg b\\). The space between the conductors is evacuated. A total charge \\(+Q\\) resides on the inner cylinder and \\(-Q\\) resides on the outer shell. Which of the following expressions gives the capacitance per unit length \\(\\dfrac{C}{L}\\) of this capacitor in terms of \\(a\\), \\(b\\), and fundamental constants?"
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url: "https://nerd-notes.com/ubq/118258/"
date_modified: "2026-08-04T08:08:28+00:00"
---

# A long cylindrical capacitor of length \(L\) consists of a solid inner conducting cylinder of radius \(a\) and a thin coaxial outer conducting cylindrical shell of radius \(b\), where \(L \gg b\). The space between the conductors is evacuated. A total charge \(+Q\) resides on the inner cylinder and \(-Q\) resides on the outer shell. Which of the following expressions gives the capacitance per unit length \(\dfrac{C}{L}\) of this capacitor in terms of \(a\), \(b\), and fundamental constants?

A long cylindrical capacitor of length \(L\) consists of a solid inner conducting cylinder of radius \(a\) and a thin coaxial outer conducting cylindrical shell of radius \(b\), where \(L \gg b\). The space between the conductors is evacuated. A total charge \(+Q\) resides on the inner cylinder and \(-Q\) resides on the outer shell. Which of the following expressions gives the capacitance per unit length \(\dfrac{C}{L}\) of this capacitor in terms of \(a\), \(b\), and fundamental constants?

![Cross-sectional diagram of a coaxial cylindrical capacitor viewed along its central longitudinal axis. Two concentric circles are centered on the origin. The inner circle is filled with light gray shading and has radius a, with a solid black arrow extending from the center origin to the boundary of the inner circle labeled a. The outer circle has radius b, shown as a thin black line, with a dashed arrow extending from the center origin to the outer circle boundary labeled b. The region between the two circles is white. A label +Q is placed inside the inner shaded circle. A label -Q is placed near the outer boundary of the outer circle. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830908-zJDDKG.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118258/*