A) \[3\sqrt{3}\]
B) \[\frac{\sqrt{3}}{3\sqrt{2}}\]
C) \[\frac{1}{3\sqrt{3}}\]
D) \[\sqrt{3}\]
Correct Answer: C
Solution :
[C]Electric field due to long wire is \[\frac{\lambda }{2\pi {{\in }_{0}}r'}\] |
There are two wire one along x and one along y axis |
So net \[E={{\vec{E}}_{1}}+{{\vec{E}}_{2}}\] where \[{{E}_{1}}\] and \[{{E}_{2}}\] is electric field due to each wire |
Where \[{{\vec{E}}_{2}}=\frac{\lambda }{2\pi {{\in }_{0}}\sqrt{3}x}\hat{j},\] \[{{\vec{E}}_{1}}=\frac{3\lambda }{2\pi {{\in }_{0}}x}\hat{i}\]\[\vec{E}=\frac{3\lambda }{2\pi {{\in }_{0}}x}\hat{i}+\frac{\lambda }{2\pi {{\in }_{0}}x\sqrt{3}}\hat{j}\] |
\[\theta \] is the angle that \[{{E}_{net}}\]made by positive x- axis |
\[\tan \theta =\frac{{{E}_{y}}}{{{E}_{x}}}=\frac{1}{\sqrt{3}}\div 3=\frac{1}{3\sqrt{3}}\] |
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