question_answer

Find the electric field vector at P (a, a, a) due to three infinitely long lines of charges along the x, y and z- axes, respectively. The charge density, i.e., charge per unit length of each wire is \[\lambda .\]

A) \[\frac{\lambda }{3\pi {{\varepsilon }_{0}}a}\left( \hat{i}+\hat{j}+\hat{k} \right)\]

B)        \[\frac{\lambda }{2\pi {{\varepsilon }_{0}}a}\left( \hat{i}+\hat{j}+\hat{k} \right)\]

C) \[\frac{\lambda }{2\sqrt{2}\pi {{\varepsilon }_{0}}a}\left( \hat{i}+\hat{j}+\hat{k} \right)\]

D) \[\frac{\sqrt{2}\lambda }{\pi {{\varepsilon }_{0}}a}\left( \hat{i}+\hat{j}+\hat{k} \right)\]