Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in the figure (Figure 1) .
Find an expression for the electric field E⃗ at the center of the semicircle.
Hint: A small piece of arc length Δs spans a small angle Δθ=Δs /R, where R is the radius.
Express your answer in terms of the variables Q, L, unit vectors i^, j^, and appropriate constants.
The Attempt at a Solution
I drew a picture and established a coordinate system. Then I drew the vector of the electric fields at two point charges at point P. Then I saw that the y components of the field will cancel because of the symmetry. I then wrote what the field should be in terms of x. I'm not sure what to do now or how to get to a point where I could integrate.