Charge over a non-conducting ring is distributed so that the linear charge density varies as  λ=λ0sinθ. What is the direction of force on a charge q0 placed at the center?

For θ≤θ<π,  λ is positive and symmetrically distributed with respect to y-axis. Similarly for π≤θ<2π,  λ is negative and symmetrically distributed about y-axis. Hence direction of electric field Enet at O due to charge distribution is in downward direction. If q0 is '−',  Fq0 upward. If q0  is  '+',  Fq0  downward.