Q$.1$ For an infinitely long rectangular metal pipes sides a and $b$ is grounded but one end at $x=0$ is maintained at a specified potential $V_0(y,z).$ Determine charge density $(y)$ on the strip at $x=0.$ Assuming it is the conductor at constant potential $V_0?$

Q$.2$ Find a solution to the following partial differential equation.

$gra{d}^2{u}^3=\frac{de{l}^2{u}^3}{del{x}^2}+\frac{de{l}^2{u}^3}{del{y}^2}=0$

$u_3(0,y)=0,u_3(L,y)=0,u_3(x,0)=0,u_3(x,H)=f_2(x)$