Problem $6$

Assume a rectangular conducting sheet of conductivity $,$ width a and height $b.$ A potential difference $V_o$ is applied to the side edges, while the top and bottom edges are not enforced to any specific

$v$

potential, as shown in figure. Find

a$)$ The potential distribution

b$)$ The current density everywhere within the sheet $($hint: Solve Laplace's equation in Cartesian coordinates subject to appropriate boundary conditions$)$