The plates of a spherical capacitor have radii 43.5 mm and 46.7 mm.?

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The plates of a spherical capacitor have radii 43.5 mm and 46.7 mm. (a) Calculate the capacitance in picofarads. (b) What must be the plate area in square centimeters of a parallel-plate capacitor with the same plate separation and capacitanc

1 Answer

  • C = (4πε0)(ab/(a-b)) = (4*pi*8.85*10^-12)*[(43.5*46.7*10 ^-6)/[(46.7-43.5)*10^-3] = 7.076*10 ^-11 f or

    Required capacitance = 70.76 pF

    Equivalent parallel cpacitance should have area A given by

    (8.85*10^-12)*A/(3.2*10^-3) = 70.76*10^-12 or

    A = [70.76*3.2*10^-3]/8.85 = 0.0256 m^2 = 256 cm^2

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