$13\mathrm{.}21$ Application: Surface Currents Induced by an Obliquely Incident Wave. A plane wave impinges on a perfectly conducting surface at $30$ to the normal. The amplitude of the incident electric field intensity is $10\frac{V}{m}$ and the wave propagates in free space. Assume the surface is in the $x-y$ plane and calculate:

$($a$)$ The surface current density $(\frac{A}{m})$ produced by the field if the polarization is perpendicular and the incident electric field intensity is in the positive $y$ direction.

$($b$)$ The surface current density for parallel polarization if the incident magnetic field intensity is in the positive $y$ direction.