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