Question

A parallel plate air condenser consists of two circular plates of diameter 8 cm. At what distance should the plates be placed so as to have the same capacity as that of a sphere of diameter 20 cm ?

• A. 2 mm
• B. 4 mm
• C. 2 cm
• D. 4 cm

Answer 1

The correct option is B 4 mm

We know $C=\frac{l_{0}A}{d}$ for parallel plates
for sphere $V=\frac{kQ}{R}$
$C=\frac{Q}{V}=\frac{QR}{kQ}=\frac{R}{k}$
$\Rightarrow \frac{R}{k}=\frac{l_{0}A}{d}$
$\Rightarrow \frac{10\times {10}^{-2}}{9\times {10}^9}=\frac{l_0\times \pi (4\times {10}^{-2}{)}^2}{x}$
$\Rightarrow x=\frac{8.85\times {10}^{-12}\times 3.14\times 16\times {10}^{-4}\times 9\times {10}^9}{10\times {10}^{-2}}$
$\Rightarrow x=4\times {10}^{-3}$