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AP Physics C: E&M
11.3 Resistance, Resistivity, and Ohm’s Law
11.1 Electric Current
AdvancedMCQMathematical13.5k
Cross section of concentric spherical shells with non-uniform conductivity.
Cross section of concentric spherical shells with non-uniform conductivity.
Two concentric, thin conducting spherical shells have inner radius \(a\) and outer radius \(b\), respectively. The region between the shells (\(a \le r \le b\)) is filled with a material whose conductivity varies radially according to \(\sigma(r) = \sigma_0 \left(\dfrac{a}{r}\right)\), where \(\sigma_0\) is a positive constant and \(r\) is the radial distance from the center. A constant potential difference \(V_0\) is maintained between the inner and outer shells. Which of the following expressions represents the total leakage current \(I\) flowing radially between the two shells?

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