Question

The distance between the plates of a circular parallel plate capacitor of diameter 40mm whose capacity is equal to that of a metallic sphere of radius 1m will be

Answer 1

capacitance of spherical capacitor is given by

$C = 4\pi \epsilon_o R$

here we have

$C = \frac{1}{9*10^9} = 1.11*10^{-10} F$

now the capacitance of parallel plate capacitor is given as

$C = \frac{epsilon_o A}{d}$

here area of the plate is given as

$A = \pi r^2 = \pi * 0.020^2$

now we have

$C = \frac{\epsilon_o *\pi * 0.020^2}{d}$

now the capacitance is same as above

$4 \pi \epsilon_o R = \frac{\epsilon_o * \pi * 0.020^2}{d}$

$4 * 1 = \frac{0.020^2}{d}$

$d = 1* 10^{-4} m = 0.1 mm$

so the distance between the plates is 0.1 mm