Let's 3D ise it (my first EM problem)

Find the electric field at the axial position of Circular ring at a distance $z$ from the centre of the ring.The charge distribution varies as $\lambda = \lambda _0 \cos\theta$ where theta is the angle made by radius vector of Ring with positive $x$ -axis

Details and Assumptions :

• Take $z=\sqrt 3 \text{ m}$

• Radius of ring $R=1 \text{ m}$

• $\lambda _0 = 2$

• Find the absolute value of your answer.

• Ring's axis lies on $z$ -axis and center lies at origin.