Electric filed:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{{\mathbf{r}}^{\mathbf{2}}}}$

Consider a point with the point **z**, located on the positive z-axis. The ring has a radius **a**. An electric field vector originating from an element of charge on the ring makes an angle θ with the z-axis.

The adjacent side has a length z, the opposite side has a length **a** and the hypotenuse is equal to (z^{2} + a^{2})^{(1/2)}. The net electric field is directed along the z-axis.

Consider a uniformly charged ring in the *xy* plane, centered at the origin. The ring has radius **a** and positive charge **q** distributed evenly along its circumference.

What is the magnitude of the electric field along the positive *z* axis?

Use k in your answer where:

$\mathbf{k}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}{\mathbf{\pi \epsilon}}_{\mathbf{0}}}$

E(x) = ______