Considering $∇^2U=0$ for a rectangular plate with a maximum length of $a$ and width of $b$ respectively.
Following are the boundary conditions:
for $y=0$
$U_y = 0$ within $0<x<a/2$ and $U = -V_o$ within $a/2<x<a$
for $y=b$
$U = V_0$ within $0<x<a/2$ and $U_y = 0$ within $a/2<x<a$
for $x = 0$ & $x = a$, $U_x = 0$
$Vo$ is a constant. What is the solution$(U(x,y))$?
The mid-plane boundary condition will be when the rectangle will split along $y$ (At $x = a/2$)?
What will be the general solution to assume in this case?