Question

If the capacity of a spherical conductor is $1$ picofarad then its diameter is :

• A. $18\times {10}^{-3}m$
• B. $9\times 10^{-3}m$
• C. $4.5\times 10^{-3}m$
• D. None of these

Answer 1

Answer: (A)

Capacitance of conductor $C=1pF$
$=1\times 10^{-12}F$
The capacitance of a spherical conductor is
$C=4\pi {\epsilon }_{0}r$ or
$1\times 10^{-12}=4\pi {\epsilon }_{0}r$
so, $r=\frac{1\times 10^{-12}}{4\pi {\epsilon }_0}$
$=9\times 10^9\times 1\times 10^{-12}$
$=9\times 10^{-3}m$
so, diameter $=2r=2\times 9\times 10^{-3}$
$=18\times 10^{-3}m$
(where $\frac{1}{4\pi {\epsilon }_0}=9\times 10^{9}N{m}^2/C^2$ )