A semicircular wire is uniformly charged with linear charge density dependent on the angle θ from y-direction as λ=λ0|sin⁡θ|, where λ0 is a constant. The electric field intensity at the centre of the arc is

Lets take an element at angle dθ as shown. Electric field due to this element isdE=dqR2Horizontal component dE sin θ will be cancelled out with opposite element, and dE cosθ components get added up. So E=∫θ=−π/2θ=π/2 dEcos⁡θ=2∫θ=0θ=π/2 Kλ0sin⁡θR2Rdθcos⁡θE→=λ04πε0R(−j^)