Find the distance d (in mm) between the plate | vedclass

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(B) The capacitance of a parallel plate capacitor is given by $C_p = \frac{\epsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plates and $r$ is

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$0.1$

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(B) The capacitance of a parallel plate capacitor is given by $C_p = \frac{\epsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plates and $r$ is the radius of the plates.Given diameter $= 40\, mm$,so radius $r = 20\, mm = 20 	imes 10^{-3}\, m$.The capacitance of an isolated metallic sphere is given by $C_s = 4\pi \epsilon_0 R$,where $R = 1\, mm = 1 	imes 10^{-3}\, m$.Equating the two capacitances: $\frac{\epsilon_0 A}{d} = 4\pi \epsilon_0 R$.Substituting $A = \pi r^2$: $\frac{\pi r^2}{d} = 4\pi R$.Solving for $d$: $d = \frac{r^2}{4R}$.Substituting the values: $d = \frac{(20 	imes 10^{-3})^2}{4 	imes 1 	imes 10^{-3}} = \frac{400 	imes 10^{-6}}{4 	imes 10^{-3}} = 100 	imes 10^{-3}\, m = 0.1\, mm$.

Find the distance $d$ (in $mm$) between the plates of a parallel plate capacitor with a plate diameter of $40\, mm$,such that its capacitance is equal to the capacitance of a metallic sphere of radius $1\, mm$.

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