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]

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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?