Question

The capacitance of a spherical conductor of radius $1 \,m$ is

• A. $9 \times 10^{-9} \, F$
• B. $10 \,\mu F$
• C. $1.1 \times 10^{-10} \, F$
• D. $1 \times 10^{-6} \, F$

Answer 1

Answer: (C)

The capacitance of a spherical conductor of radius $R$ is
$C=4\pi\varepsilon_{0}R$ or $C=\frac{R}{\frac{1}{4\pi\varepsilon_{0}}}$
Here, $R=1\,m$, $\frac{1}{4\pi\varepsilon_{0}}=9 \times 10^{9}\,N\,m^{2}\,C^{-2}$
$\therefore C=\frac{1}{9 \times10^{9}}=0.11\times10^{-9}\,F$
$=1.1 \times10^{-10}\,F$