$2.(10$ points$)($a$)$ Show that an expression for the height of rise of water in a capillary tube of radius r balances the difference in pressure across the air$-$water interface with the surface tension around the interface. Define all terms

$($b$)$ Consider a capillary tube with a square cross section. Write an expression for the height of rise of water in the tube as a function of the length of the tube sides, L$,$ assuming perfect wetting.