A) Zero
B) \[\frac{q({{Q}_{2}}-{{Q}_{1}})(\sqrt{2}-1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\]
C) \[\frac{q\sqrt{2}({{Q}_{1}}+{{Q}_{2}})}{4\pi {{\varepsilon }_{0}}R}\]
D) \[\frac{q({{Q}_{1}}+{{Q}_{2}})(\sqrt{2}+1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\]
Correct Answer: B
Solution :
[b] \[W=q({{V}_{O2}}-{{V}_{O1}})\] Where \[{{V}_{{{O}_{1}}}}=\frac{{{Q}_{1}}}{4\pi {{\varepsilon }_{0}}R}+\frac{{{Q}_{2}}}{4\pi {{\varepsilon }_{0}}R\sqrt{2}}\] And \[{{V}_{{{O}_{2}}}}=\frac{{{Q}_{2}}}{4\pi {{\varepsilon }_{0}}R}+\frac{{{Q}_{1}}}{4\pi {{\varepsilon }_{0}}R\sqrt{2}}\] \[\Rightarrow {{V}_{{{O}_{2}}}}-{{V}_{{{O}_{1}}}}=\frac{({{Q}_{2}}-{{Q}_{1}})}{4\pi {{\varepsilon }_{0}}R}\left[ 1-\frac{1}{\sqrt{2}} \right]\] So, \[W=\frac{q.({{Q}_{2}}-{{Q}_{1}})}{4\pi {{\varepsilon }_{0}}R}\frac{(\sqrt{2}-1)}{\sqrt{2}}\]You need to login to perform this action.
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