An isolated sphere has a capacitance of 60 pF, what is the radius of the sphere?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 54 cm
The capacitance of an isolated conducting sphere of radius R is \( C = 4\pi\varepsilon_0 R \), where \( \frac{1}{4\pi\varepsilon_0} = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).
\( \displaystyle R = \frac{C}{4\pi\varepsilon_0} = 60\times10^{-12}\,\mathrm{F}\times9\times10^{9}\,\mathrm{m\,F^{-1}} \)
\( R = 0.54\,\mathrm{m} = 54\,\mathrm{cm} \)