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 λ.

Let us consider the electric field due to wire (3) only.E→3=Eu^E→3=λ2πε0a2+a21/2i^cos⁡45∘+j^sin⁡45∘=λ22πε0a12(i^+j^)E→3=λ4πε0a(i^+j^)Similarly, electric field due to wires (1) and (2)E→1=λ4πε0a(j^+k^) and E→2=λ4πε0a(i^+k^)E→net=E→1+E→2+E→3 E→net=λ2πε0a(i^+j^+k^)