A thin semicircular ring of radius r has a positive charge . . .

Question : A thin semicircular ring of radius r has a positive charge 'q' uniformly distributed over it. The net electric field E at centre O is 

a) qj/2π²ε₀r²

b) qi/4π²ε₀r²

c) -qi/4π²ε₀r²

d) -qj/2π²ε₀r²

Doubt by Diya

Ans : d) is the correct option. 

Solution : 

The electric field at the Centre O due to the small charge element dq of the semicircle

After resolving dE into two rectangular components we can see that dE cosθ components will be cancelled out so the total magnetic field at O will be given by adding all dE sinθ components.

Hence, d) would be the correct option.