A) \[2.0\times {{10}^{-7}}J\]
B) \[1.35\times {{10}^{-7}}J\]
C) \[2.7\times {{10}^{-7}}J\]
D) \[12.1\times {{10}^{-7}}J\]
Correct Answer: B
Solution :
(b) \[1.35\times {{10}^{-7}}J\] Required work done = Change in potential energy of the system \[W={{U}_{f}}-{{U}_{i}}=k\frac{{{q}_{1}}{{q}_{2}}}{{{r}_{f}}}-k\frac{{{q}_{1}}{{q}_{2}}}{{{r}_{i}}}\] \[=k{{q}_{1}}{{q}_{2}}\left[ \frac{1}{{{r}_{f}}}-\frac{1}{{{r}_{i}}} \right]\] \[\therefore \,\,\,\,W=\left( 9\times {{10}^{9}} \right)\left( 3\times {{10}^{-9}}\times 1\times {{10}^{-9}} \right)\] \[\times \left[ \frac{1}{4\times {{10}^{-2}}}-\frac{1}{5\times {{10}^{-2}}} \right]\] \[=27\times {{10}^{-7}}\times \left( 0.05 \right)=1.35\times {{10}^{-7}}J\]
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