If the circumference of a sphere is 3 m, then the capacitance of the sphere in water is (dielectric constant…
If the circumference of a sphere is 3 m, then the capacitance of the sphere in water is (dielectric constant of water = 80)
- 4250 pF
- 2760 pF
- 2780 pF
- 424 pF
Solution
Dielectric constant of water, k = 80
Capacitance of a sphere of radius R is given by
$C=4 \pi \varepsilon_0 R$
Circumference of sphere, L = 3m
$
\begin{aligned}
& \text { Radius of sphere, } R=\frac{L}{2 \pi} \\
& \Rightarrow \quad=\frac{3}{2 \pi} \mathrm{m}
\end{aligned}
$
Capacitance, $C=4 \pi \varepsilon_0 \times \frac{3}{2 \pi}=6 \varepsilon_0 \mathrm{~F}$
Capacitance of sphere in water,
$\begin{aligned} C^{\prime} & =C \times k \\ & =80 \times 6 \varepsilon_0 \\ \Rightarrow \quad & =480 \varepsilon_0 \\ & =480 \times 8.854 \times 10^{-12} \mathrm{~F} \\ & =4249.92 \times 10^{-12} \mathrm{~F} \\ & \simeq 4250 \mathrm{pF}\end{aligned}$
Asked in: AP EAMCET 2021 (25 Aug Shift 2)
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