Casimir force on a piston

We consider a massless scalar field obeying Dirichlet boundary conditions on the walls of a two-dimensional L×b rectangular box, divided by a movable partition (piston) into two compartments of dimensions a×b and (L-a)×b. We compute the Casimir force on the piston in the limit →L∞. Regardless of the value of $a/b,$ the piston is attracted to the nearest end of the box. Asymptotic expressions for the Casimir force on the piston are derived for ab and ab.