Question

The capacitance of a metallic sphere is $1\,\mu F,$ then its radius is nearly

• A. 1.11 m
• B. 10 m
• C. 9 km
• D. 1.11 cm

Answer 1

Answer: (C)

9 km

Answer 2

For a spherical capacitor of radius $R$, the capacitance is given by $C=4 \pi \varepsilon_{0} R$ Given, $C=1 \,\mu F =1 \times 10^{-6} F$ $\Rightarrow R =\frac{C}{4 \pi \varepsilon_{0}}$ $=9 \times 10^{9} \times 1 \times 10^{-6} m$ $\Rightarrow R =9 \times 10^{3} m$ $=9 \,km$