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AP Physics C: E&M
10.4 Dielectrics
10.3 Capacitors
AdvancedMCQMathematicalConceptual15.9k
Cross section of concentric spherical shells with a radially varying dielectric.
Cross section of concentric spherical shells with a radially varying dielectric.
A spherical capacitor consists of two thin, concentric conducting spherical shells of radii \(a\) and \(b\), where \(a < b\). The region between the shells is completely filled with an inhomogeneous dielectric material whose permittivity varies with radial distance \(r\) according to \(\varepsilon(r) = \varepsilon_0 \left(\dfrac{r}{a}\right)\), where \(\varepsilon_0\) is the permittivity of free space. A charge \(+Q\) resides on the inner shell and a charge \(-Q\) resides on the outer shell. In terms of \(\varepsilon_0\), \(a\), and \(b\), which of the following is the capacitance of this spherical capacitor?

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