In cylindrical coordinates (r, θ, z), the potential V only depends on z, so we have: E = -∂V/∂z ȕz where ȕz is the unit vector in the z-direction. Taking the derivative of V(z) with respect to z, we get: ∂V/∂z = 4πkρz/(z^2 + a^2)^(3/2) where ρz is the surface charge density on the annulus.