Given that, linear charge density of non-conducting ring λ=λ0cosφ, and Azimuthal angle =φ Consider two elements of length (dl=Rdφ) are taken symmetrically at angle φ on both sides as shown in figure. Here, dE1=dE2 and sinφ components cancelled out each other. Charge on the elements, dq1=λdl=(λ0cosφ)rdφ . . . (i)
Now, net field at centre of ring due to both elements, dE=2dE1cosφ⇒