A) \[4\times {{10}^{-3}}m\]
B) \[1\times {{10}^{-3}}m\]
C) \[1cm\]
D) \[1\times {{10}^{-3}}cm\]
Correct Answer: B
Solution :
Capacity of spherical conductor of 20 cm diameter \[{{C}_{1}}=4\pi {{\varepsilon }_{0}}r=4\pi {{\varepsilon }_{0}}\times 10\] Capacity of parallel plate air capacitor \[{{C}_{2}}=\frac{{{\varepsilon }_{0}}A}{d}=\frac{{{\varepsilon }_{0}}[\pi {{(2)}^{2}}]}{d}=\frac{{{\varepsilon }_{0}}\times 4\pi }{d}\] Hence \[{{C}_{1}}={{C}_{2}}\] Þ \[40\pi {{\varepsilon }_{0}}=\frac{4\pi {{\varepsilon }_{0}}}{d}\]Þ \[d={{10}^{-3}}m\]
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