If the circumference of a sphere is 2 m,find | vedclass

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(D) Given,circumference of the sphere $2\pi R = 2 \ m$. So,$R = \frac{1}{\pi} \ m$. The capacitance of a spherical conductor in a medium is given by $

Vedclass · Accepted Answer

$2828$

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(D) Given,circumference of the sphere $2\pi R = 2 \ m$. So,$R = \frac{1}{\pi} \ m$. The capacitance of a spherical conductor in a medium is given by $C = 4\pi \varepsilon_0 K R$. We know that $\frac{1}{4\pi \varepsilon_0} = 9 	imes 10^9 \ N \cdot m^2/C^2$,so $4\pi \varepsilon_0 = \frac{1}{9 	imes 10^9}$. Substituting the values: $C = \frac{1}{9 	imes 10^9} 	imes 80 	imes \frac{1}{\pi}$. $C = \frac{80}{9 	imes 3.14159 	imes 10^9} \approx 2.828 	imes 10^{-9} \ F$. Converting to $pF$ $(1 \ F = 10^{12} \ pF)$: $C = 2.828 	imes 10^{-9} 	imes 10^{12} \ pF = 2828 \ pF$.

If the circumference of a sphere is $2 \ m$,find the capacitance of the sphere in water in $pF$. (Take dielectric constant of water $K = 80$)

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