Question

Capacitance of an isolated metallic sphere having radius $8.1$ mm is nearly :

• A. $9\times {10}^{-9}$ $\mu F$
• B. $9\times {10}^{-6}$ $\mu F$
• C. $9\times {10}^{-1}$ $pF$
• D. $9\times {10}^{-5}$ $\mu F$

Answer 1

Answer: (D)

$9\times {10}^{-5}$ $\mu F$

Given,

$r=8.1mm$

The capacitance of an isolated metallic sphere is given by

$C=4\pi {\epsilon }_{0}r$

$C=4\times 3.14\times 8.85\times {10}^{-12}\times 8.1\times {10}^{-3}$

$C=900\times {10}^{-13}F$

$C=9\times {10}^{-5}\mu F$

The correct option is D.