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Q.
The capacitance of a metallic sphere is $ 1\,\mu F, $ then its radius is nearly
ManipalManipal 2010Electrostatic Potential and Capacitance
Solution:
For a spherical capacitor of radius $R$, the capacitance is given by
$C=4 \pi \varepsilon_{0} R$
Given, $C=1 \,\mu F =1 \times 10^{-6} F$
$\Rightarrow R =\frac{C}{4 \pi \varepsilon_{0}} $
$=9 \times 10^{9} \times 1 \times 10^{-6} m $
$\Rightarrow R =9 \times 10^{3} m $
$=9 \,km$