http://i47.tinypic.com/syxkr7.png

From the above figure,

∇.(∇∅)=0

i.e. http://www.mathhelpforum.com/math-he...be85ba44a6.png

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-

http://i56.tinypic.com/293zw4h.jpg