[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 \cdot^{2}] 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)=E_{0}[\cos (k z-\omega t)-\cos (k z+\omega t)] \hat{ x }, \quad(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)
P=\frac{1}{A} \frac{\Delta p}{\Delta t}=\frac{1}{2} \epsilon_{0} E_{0}^{2}=\frac{I}{c} (9.64)