The capacitance of a metallic sphere is 1 μ F, then its radius is nearly

Question

The capacitance of a metallic sphere is 1 μ F, then its radius is nearly (A) 1.11 m (B) 10 m (C) 9 km (D) 1.11 cm

Tardigrade Admin · Accepted Answer

For a spherical capacitor of radius R, the capacitance is given by C=4 π ε0 R Given, C=1 μ F =1 × 10-6 F ⇒ R =(C/4 π ε0) =9 × 109 × 1 × 10-6 m ⇒ R =9 × 103 m =9 km

Q. The capacitance of a metallic sphere is $1 μ F,$ then its radius is nearly

1.11 m

10 m

9 km

1.11 cm

For a spherical capacitor of radius $R$ , the capacitance is given by
$C = 4 π ε_{0} R$
Given, $C = 1 μ F = 1 \times 1 0^{- 6} F$
$\Rightarrow R = \frac{C}{4 π ε _{0}}$
$= 9 \times 1 0^{9} \times 1 \times 1 0^{- 6} m$
$\Rightarrow R = 9 \times 1 0^{3} m$
$= 9 km$

Q. The capacitance of a metallic sphere is 1μF, then its radius is nearly