Two infinitely long, thin straight wires, each carrying a uniform positive linear charge density + , are placed along the X and Y axes respectively in free space. What is the magnitude of the net electric field at a point P(a, a) in the XY plane?

Step-by-step solution

The point P(a, a) is at a perpendicular distance a from the X-axis and a perpendicular distance a from the Y-axis. The electric field due to the wire along the X-axis at point P is directed along the positive Y-direction: E ₁ = 2 ₀ a j The electric field due to the wire along the Y-axis at point P is directed along the positive X-direction: E ₂ = 2 ₀ a i Since these two electric field vectors are perpendicular to each other, the magnitude of the net electric field is given by vector addition: E_ net = E₁^2 + E₂^2 E