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Solved: The inner cylinder of a long, cylindrical
Chapter 24, Problem 70P(choose chapter or problem)
The inner cylinder of a long, cylindrical capacitor has radius \(r_a\) and linear charge density \(+\lambda\). It is surrounded by a coaxial cylindrical conducting shell with inner radius \(r_{b}\) and linear charge density \(-\lambda\) (see Fig. 24.6).
(a) What is the energy density in the region between the conductors at a distance from the axis?
(b) Integrate the energy density calculated in part (a) over the volume between the conductors in a length of the capacitor to obtain the total electric-field energy per unit length.
(c) Use Eq. (24.9) and the capacitance per unit length calculated in Example 24.4 (Section 24.1) to calculate U/L Does your result agree with that obtained in part (b)?
Questions & Answers
QUESTION:
The inner cylinder of a long, cylindrical capacitor has radius \(r_a\) and linear charge density \(+\lambda\). It is surrounded by a coaxial cylindrical conducting shell with inner radius \(r_{b}\) and linear charge density \(-\lambda\) (see Fig. 24.6).
(a) What is the energy density in the region between the conductors at a distance from the axis?
(b) Integrate the energy density calculated in part (a) over the volume between the conductors in a length of the capacitor to obtain the total electric-field energy per unit length.
(c) Use Eq. (24.9) and the capacitance per unit length calculated in Example 24.4 (Section 24.1) to calculate U/L Does your result agree with that obtained in part (b)?
ANSWER:Solution 70P
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