From the above figure,

∇.(∇∅)=0

i.e.

Given boundary conditions:

$\displaystyle \displaystyle \frac{\partial \varphi}{\partial n} = 0$ (normal direction)

$\displaystyle \varphi=0 $ at grounded electrode

$\displaystyle \varphi=\varphi( t)$ at upper electrode

Now how can I solve?

I have tried as follows using separation of variable-