a charge Q is distributed uniformly along a line segment bent into a semi circle of radius X.show that the field at the center of the circle is given by E=Exi+Eyj=Q/2π2ε˳̻R2

Answer 1

I assume you are taking calculus.

You integrate a dl segement along the wire, however, due to symettry, all the components of field not along the semicircle axis cancel out. So you are integrating just the sine function of the angle...
http://www.phys.uri.edu/gerhard/PHY204/tsl329.pdf