ES potential two parallel plates

[Knot Head]

Derive the electrostatic potential between two flat plates in electrolyte solution. The surface potential at the plate surfaces is low.

I think this problem uses the Poisson equation for electostatic potential, but the one I came up with was wrong. It involves the hyperbolic cos. (cosh)

 

[Knot Head]

\alpha

Derive the electrostatic potential between two flat plates in electrolyte solution. The surface potential at the plate surfaces is low.

I think this problem uses the Poisson equation for electostatic potential, but the one I came up with was wrong. It involves the hyperbolic cos. (cosh)

\Phi'(\(pmR)=\pm2S_{R}/\lambda_{GC}
S_{R}=sgn(\sigma_{R}
\Phi'(0)=0

and Poisson-Boltzman
\Psi=\betaq\phi for two identical charged plates is given by
-\Psi''(z)+sinh \Psi(z)=0
the first integral= cosh \Psi
the interaction between the two plates is:
P=2nT(\alpha-1)=T\delta\alpha/4\pil\lambda

I keep going around and around but I'm not even close. Any advice would be greatly appreciated.