## [HW4 Q2.2/2.3]

## Summary

Initial boundary conditions / Implementation of `\dfrac{d\psi (x=h/2)}{dx}=0`

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## Details

Q2.2: I solved the Poisson-Boltzmann equation with initial boundary conditions for `\psi (x=0)=\psi(0)`

and `\dfrac{d\psi (x=0)}{dx}`

being my guessing parameter and it works well. I then looked for a value of `\dfrac{d\psi (x=0)}{dx}`

giving a solution satisfying `\dfrac{d\psi (x=h/2)}{dx}=0`

, which must be valid in the middle between the two plates. The solution I obtained satisfies equation 6 as well.

Q2.3: My result is not realistic (`\psi`

=40mV over whole gap). It seems that my solution doesnt work for realistic parameter values.

Is the implementation of the boundary condition `\dfrac{d\psi (x=h/2)}{dx}=0`

correct? I hesitated with this part cause we are looking for a solution to satisfy eq. 6. However, I couldnt find another way to implement both conditions simultaneously.