Aspherical capacitor consists of a solid conducting sphere

Chapter , Problem 86

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Aspherical capacitor consists of a solid conducting sphere that has a radius and a charge and a concentric conducting spherical shell that has an inner radius and a charge The space between the two is filled with two different dielectric materials of dielectric constants and The boundary between the two dielectrics occurs a distance from the center. (a) Calculate the electric field in the regions and (b) Integrate the expression to obtain the potential difference, between the two conductors. (c)Use to obtain an expression for the capacitance of this system. (d) Show that your answer from Part (c) simplifies to the expected one if equals

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