Uniformly Polarized disk on a conducting plane (E-Field)

[jegues]

Homework Statement

A uniformly polarized dielectric disk surrounded by air is lying at a conducting plane, as shown in the figure. The polarization vector in the is,

[tex]\vec{P} = P \hat{k},[/tex]

the disk radius is a, and the thickness d. Calculate the electric field intensity vector along the disk axis normal to the conducting plane (z-axis).

Homework Equations

The Attempt at a Solution

See the second figure attached for their solution and a picture of the problem, and the first figure for my attempt.

Are our answers the same? I can't seem to get it exactly in the form they have but it looks relatively close.

Can someone confirm?
Is my answer equivalent to theirs? If no what did I do wrong?

 

[lightgrav]

your E1(z) is ok, your E2(z) is ok. your re-writing of them , as they are added, makes them seem more complicated, rather than terms canceling (to simplify).