A) \[\frac{{{Q}^{2}}}{4\pi {{\in }_{0}}}\left( 1+\frac{1}{\sqrt{3}} \right)\]
B) \[\frac{{{Q}^{2}}}{4\pi {{\in }_{0}}}\left( 1+\frac{1}{\sqrt{5}} \right)\]
C) \[\frac{{{Q}^{2}}}{2\sqrt{2}\pi {{\in }_{0}}}\]
D) \[\frac{{{Q}^{2}}}{4\pi {{\in }_{0}}}\]
Correct Answer: B
Solution :
\[W=VQ=\frac{1}{4\pi {{\varepsilon }_{0}}}{{Q}_{2}}\left[ \frac{1}{2}+\frac{1}{2}+\frac{1}{2\sqrt{5}}+\frac{1}{2\sqrt{5}} \right]\] |
\[=\frac{1}{4\pi {{\varepsilon }_{0}}}{{Q}_{2}}\left[ \frac{1}{2}+\frac{1}{2}+\frac{1}{2\sqrt{5}} \right]\] |
\[\therefore \] \[W=\frac{{{Q}_{2}}}{4\pi {{\varepsilon }_{0}}}\left[ 1+\frac{1}{\sqrt{5}} \right].\] |
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