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(A) Dielectric constant of water,$k = 80$. Capacitance of an isolated sphere of radius $R$ in vacuum is given by $C = 4 \pi \varepsilon_0 R$. Circumfe

Vedclass · Accepted Answer

$4250$

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(A) Dielectric constant of water,$k = 80$. Capacitance of an isolated sphere of radius $R$ in vacuum is given by $C = 4 \pi \varepsilon_0 R$. Circumference of the sphere,$L = 2 \pi R = 3 \ m$. Therefore,the radius of the sphere is $R = \frac{3}{2 \pi} \ m$. Capacitance in vacuum,$C = 4 \pi \varepsilon_0 	imes \frac{3}{2 \pi} = 6 \varepsilon_0 \ F$. Capacitance of the sphere in water,$C' = k 	imes C$. $C' = 80 	imes 6 \varepsilon_0 = 480 \varepsilon_0 \ F$. Substituting $\varepsilon_0 = 8.854 	imes 10^{-12} \ F/m$: $C' = 480 	imes 8.854 	imes 10^{-12} \ F = 4249.92 	imes 10^{-12} \ F \approx 4250 \ pF$.

If the circumference of a sphere is $3 \ m$,then the capacitance of the sphere in water is (dielectric constant of water = $80$) (in $pF$)

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