Potential in the three regions of an infinite slab

[workhorse123]

Homework Statement

The charge density in the region
-z’<z<z’
depends only on z; that is,
p=p’cos(pi z/z’)
where p’ and z’ are constants. Determine the potential in all regions of space

Relevant Equations

Poisons equation, laplace equation

for the boundary conditions for this problem I understand that Electric field and Electric potential will be continuous on the boundaries.
I also know that I can set the reference point for Electric potential, wherever it is convenient. This gives me the fifth boundary condition. I am confused at where I find the last boundary condition.

 

[TSny]

Welcome to PF!
If possible, please type in your work using Latex, rather than posting snapshots of your work. Additional guidelines for posting in the homework forums can be found here.

You cannot arbitrarily choose a "zero point" for the electric field like you can with the potential. However, can you justify the condition ##E_{\text{at} \, z = 0} = 0## from the symmetrical nature of the charge distribution in this problem?