A) \[4\times {{10}^{-3}}m\]
B) \[1\times {{10}^{-3}}m\]
C) 1cm
D) \[1\times {{10}^{-3}}cm\]
Correct Answer: B
Solution :
\[{{r}_{1}}=\frac{4}{2}=2\,cm=2\times {{10}^{-2}}m\] \[{{r}_{2}}=\frac{20}{2}=10\,cm=10\times {{10}^{-2}}m\] 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\[=1\times {{10}^{-3}}m\].
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