Chapter 9: Problem 11
Let the internal dimensions of a coaxial capacitor be \(a=1.2 \mathrm{~cm}, b=4 \mathrm{~cm}\), and \(l=40 \mathrm{~cm}\). The homogeneous material inside the capacitor has the parameters \(\epsilon=10^{-11} \mathrm{~F} / \mathrm{m}, \mu=10^{-5} \mathrm{H} / \mathrm{m}\), and \(\sigma=10^{-5} \mathrm{~S} / \mathrm{m}\). If the electric field intensity is \(\mathbf{E}=\left(10^{6} / \rho\right) \cos 10^{5} t \mathbf{a}_{\rho} \mathrm{V} / \mathrm{m}\), find \((a) \mathbf{J} ;(b)\) the total conduction current \(I_{c}\) through the capacitor; \((c)\) the total displacement current \(I_{d}\) through the capacitor; \((d)\) the ratio of the amplitude of \(I_{d}\) to that of \(I_{c}\), the quality factor of the capacitor.
Short Answer
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