A) \[\frac{27}{20}{{\lambda }_{0}}\]
B) \[\frac{20}{27}{{\lambda }_{0}}\]
C) \[\frac{16}{25}{{\lambda }_{0}}\]
D) \[3\Omega \]
Correct Answer: C
Solution :
Given planes are \[X=\frac{\sqrt{3}}{4}L\] and \[{{l}_{sys}}={{l}_{1}}+{{l}_{2}}+{{l}_{3}}\] On comparing with \[=M\times {{(0)}^{2}}+M\times {{(X)}^{2}}+M\times {{(0)}^{2}}\], we get \[{{n}_{1}}=2\hat{i}-\hat{j}+\hat{k}\] and \[{{n}_{2}}=\hat{i}+\hat{j}+2\hat{k}\] \[{{V}_{1}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{Q}_{1}}}{{{R}_{1}}}\] \[{{V}_{2}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{Q}_{2}}}{{{R}_{2}}}\] \[{{V}_{1}}={{V}_{2}}\] \[=\frac{2-1+2}{\sqrt{4+1+1}\sqrt{1+1+4}}=\frac{3}{\sqrt{6}\times \sqrt{6}}=\frac{3}{6}=\frac{2}{1}\]\[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] \[s=\frac{{{t}^{4}}}{4}\]
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