Question

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

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

Answer 1

Answer: (B)

$r_1=\frac{4}{2}=2cm=2\times {10}^{-2}m$ $r_2=\frac{20}{2}=10cm=10\times {10}^{-2}m$ Capacity of parallel plate capacitor = capacitor of spherical capacitor i.e., $\frac{{\epsilon }_{0}A}{d}=4\pi {\epsilon }_0{r}_2$ or $\frac{{\epsilon }_0\pi r_1^2}{d}=4\pi {\epsilon }_0{r}_2$ or $d=\frac{r_1^2}{4r_2}$ $\therefore$ $d=\frac{{(2\times {10}^{-2})}^2}{4\times 10\times {10}^{-2}}=\frac{4\times {10}^{-4}}{4\times {10}^{-1}}=1\times {10}^{-3}m$ Distance between plates $=1\times {10}^{-3}m$ .