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AP Physics C: E&M
10.4 Dielectrics
10.3 Capacitors
AdvancedMCQMathematical19.7k
Cross section of a spherical capacitor with a radially graded dielectric.
Cross section of a spherical capacitor with a radially graded dielectric.
A spherical capacitor consists of a solid conducting sphere of radius \(a\) surrounded by a concentric conducting spherical shell of inner radius \(b\). The space between the conductors (\(a < r < b\)) is filled with a non-uniform dielectric material whose dielectric constant varies radially according to \(\kappa(r) = \kappa_0 \dfrac{a}{r}\), where \(\kappa_0\) is a dimensionless constant. Which of the following expressions represents the capacitance of this capacitor?

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