A) \[2.7\times {{10}^{10}}\,J\]
B) \[9.9\times {{10}^{10}}\,J\]
C) \[10.8\times {{10}^{10}}\,J\]
D) \[5.4\times {{10}^{10}}\,J\]
Correct Answer: B
Solution :
Key Idea: Work done is equal to potential energy. Potential energy \[(U)\] is given by \[U=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}{{q}_{2}}}{r}\] For three sets of charges \[U={{U}_{1}}+{{U}_{2}}+{{U}_{3}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\] \[({{q}_{1}}{{q}_{2}}+{{q}_{2}}{{q}_{3}}+{{q}_{3}}{{q}_{1}}).\frac{1}{r}\] \[\Rightarrow \]\[U=\frac{1}{4\pi {{\varepsilon }_{0}}}(1\times 2+2\times 3+3\times 1)\left( \frac{1}{0.5}-\frac{1}{1} \right)\] \[=9\times {{10}^{9}}\times 11\] \[=9.9\times {{10}^{10}}J\]
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