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(B) The capacitance of a parallel plate capacitor is given by $C = \frac{\varepsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plate.Given diame

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$1 	imes 10^{-3} \ m$

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(B) The capacitance of a parallel plate capacitor is given by $C = \frac{\varepsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plate.Given diameter of the plate is $4 \ cm$,so radius $r = 2 \ cm = 2 	imes 10^{-2} \ m$.Area $A = \pi (2 	imes 10^{-2})^2 = 4\pi 	imes 10^{-4} \ m^2$.The capacitance of a sphere of radius $R$ is $C = 4\pi \varepsilon_0 R$.Given diameter of the sphere is $20 \ cm$,so radius $R = 10 \ cm = 0.1 \ m$.Equating the two capacitances: $\frac{\varepsilon_0 A}{d} = 4\pi \varepsilon_0 R$.$\frac{A}{d} = 4\pi R$.$d = \frac{A}{4\pi R} = \frac{4\pi 	imes 10^{-4}}{4\pi 	imes 0.1} = \frac{10^{-4}}{10^{-1}} = 10^{-3} \ m$.

$A$ parallel plate capacitor is made of two plates with a diameter of $4 \ cm$. What should be the distance between the two plates so that its capacitance is equal to the capacitance of a sphere with a diameter of $20 \ cm$?

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