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AP Physics C: E&M
10.3 Capacitors
AdvancedMCQMathematical21.2k
A clean cross-sectional diagram showing two parallel conducting cylinders end-on in a two-dimensional plane. On the left is a circle of radius \(R\) labeled with charge density \(+\lambda\). On the right, separated horizontally by a center-to-center distance \(d\), is an identical circle of radius \(R\) labeled with charge density \(-\lambda\). A horizontal dashed line segment connects the center of the left circle to the center of the right circle, with a double-headed dimension arrow below it labeled \(d\). A radial line segment from the center of the left circle to its top edge is labeled with radius \(R\). A horizontal axis labeled \(x\) starts at the center of the left circle and points to the right toward the right circle. No other labels, lines, text, or axes appear.
Cross section of two long parallel conducting cylinders.
Two extremely long, parallel conducting cylinders, each of radius \(R\), are oriented parallel to each other with a center-to-center separation distance \(d\), where \(d \gg R\). The two cylinders carry uniform linear charge densities of \(+\lambda\) and \(-\lambda\), respectively. Which of the following expressions represents the capacitance per unit length \(C/L\) of this two-cylinder system?

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