• # question_answer Two infinitely long charge wires with linear densities $\lambda$ & $3\lambda$ are placed along x & y axis respectively determined the $\tan \theta$ where $\theta$ is the angle that electric field at any point on the line $y=\sqrt{3}\,\,x$ make with positive x-axis. A) $3\sqrt{3}$                   B) $\frac{\sqrt{3}}{3\sqrt{2}}$ C) $\frac{1}{3\sqrt{3}}$ D) $\sqrt{3}$

[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 $\tan \theta =\frac{{{E}_{y}}}{{{E}_{x}}}=\frac{1}{\sqrt{3}}\div 3=\frac{1}{3\sqrt{3}}$