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}=2\,cm=2\times {{10}^{-2}}m $ $ {{r}_{2}}=\frac{20}{2}=10\,cm=10\times {{10}^{-2}}m $ Capacity of parallel plate capacitor = capacitor of spherical capacitor i.e., $ \frac{{{\varepsilon }_{0}}A}{d}=4\pi {{\varepsilon }_{0}}{{r}_{2}} $ or $ \frac{{{\varepsilon }_{0}}\pi r_{1}^{2}}{d}=4\pi {{\varepsilon }_{0}}{{r}_{2}} $ or $ d=\frac{r_{1}^{2}}{4{{r}_{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 $ .