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-Boltzmann
$$\Psi$$=$$\beta$$q$$\phi$$ 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$$\pi$$l$$\lambda$$

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