Question

Two non-conducting semi-infinite rods lies along the x-axis as shown in the Figure. One rod lies from x = L/2 to x = infinity and the other rod lies from x = -L/2 to and x = -infinity. The rods have charge uniformly distributed along their length with a linear density λ. What is the magnitude of the electric field at a point P located on the y-axis at y = L/2? 

Answer 1

From the symmetry in the problem we see that the x-component of the electric field at the point P is zero and that the y-component of the electric field from the two rods is twice that from one of the rods as follows,

where I used dQ = λdx and cosθ = y/r with r² = x² + y². Plugging in y = L/2 yields