[The naive explanation for the pressure of light offered in Section 9.2.3 has its flaws, as you discovered if you worked Problem 9.11. Here's another account, due originally to Planck.] A plane wave traveling through vacuum in the z direction encounters a perfect conductor occupying the region z≥0, and reflects back:
E(z,t)=E0[cos(kz−ωt)−cos(kz+ωt)]x^,(z<0).
(a) Find the accompanying magnetic field (in the region z<0).
(b) Assuming B=0 inside the conductor, find the current K on the surface z=0, by invoking the appropriate boundary condition.
(c) Find the magnetic force per unit area on the surface, and compare its time average with the expected radiation pressure (Eq. 9.64).