A) \[4\times {{10}^{2}}C\]
B) \[5\times {{10}^{-2}}C\]
C) \[2\times {{10}^{-2}}C\]
D) \[4\times {{10}^{-2}}C\]
Correct Answer: C
Solution :
\[{{C}_{1}}=4\pi {{\varepsilon }_{0}}\times {{10}^{-2}}F,{{Q}_{1}}={{10}^{-2}}C\] \[{{C}_{2}}=4\pi {{\varepsilon }_{0}}\times 2\times {{10}^{-2}}F,{{Q}_{2}}=5\times {{10}^{-2}}C\] \[\therefore \] \[V=\frac{total\text{ }charge}{total\text{ }capacity}\] \[=\frac{6\times {{10}^{-2}}}{4\pi {{\varepsilon }_{0}}\times 3\times {{10}^{-2}}}\] \[\therefore \] \[{{Q}_{1}}'={{C}_{1}}V\] \[=4\pi {{\varepsilon }_{0}}\times {{10}^{-2}}\times \frac{6\times {{10}^{-2}}}{4\pi {{\varepsilon }_{0}}\times 3\times {{10}^{-2}}}\] \[=2\times {{10}^{-2}}C\]
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