A spherical conductor placed in vacuum has capacitance of \( 3.14\times10^{-9}\,\mathrm{F} \). Its radius will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 28.3\,\mathrm{m} \)
The capacitance of an isolated spherical conductor of radius \( R \) in vacuum is \( C = 4\pi\varepsilon_{0}R \).
\( \displaystyle R = \frac{C}{4\pi\varepsilon_{0}} = 9\times10^{9} \times C = 9\times10^{9} \times 3.14\times10^{-9} = 28.3\,\mathrm{m} \)
using \( 1/(4\pi\varepsilon_{0}) = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).