Question

The diameter of each plate of an air capacitor is $4cm$. To make the capacity of this plate capacitor equal to that of $20cm$ diameter sphere the distance between the plates will be

• A. $1\times {10}^{-3}cm$
• B. $1cm$
• C. $1\times {10}^{-3}m$
• D. $4\times {10}^{-3}m$

Answer 1

Answer: (C)

$1\times {10}^{-3}m$

$r_1=\frac{4}{2}=2cm=2\times {10}^{-2}m$

$r_2=\frac{20}{2}=10cm=10\times {10}^{-2}m$

capacity of parral plate capacitor = capacitor of spherical capacitor

i.e. $\frac{{\epsilon }_{0}A}{d}=4\pi {\epsilon }_0{r}_2$

i.e. $\frac{{\epsilon }_0\pi r_1^2}{d}=4\pi {\epsilon }_0{r}_2$

$d=\frac{r_1^2}{4r_2}$

$d=\frac{(2\times {10}^{-}2{)}^2}{4\times 10\times {10}^{-}2}=1\times {10}^{-3}m$