Question

The capacitance of a conducting metallic sphere will be $1\mu F$ if its radius is nearly :

• A. $12$ km
• B. $10$ km
• C. $1.11$ km
• D. $9$ km

Answer 1

The correct option is D $9$ km

The expression of capacitance of metallic sphere is $C=4\pi {ϵ}_{0}r$ (The capacitance of a single spherical conductor means that we imagine a spherical shell of infinite radius surrounding the first conductor.)
Therefore, $r=\frac{C}{4\pi {ϵ}_0}={10}^{-6}\times 9\times {10}^9=9\times {10}^{3}m=9km$