# Wave guide boundary conditions

Why only the normal component of Electric field and the parallel component of Magnetic field exist at the surface of a wave guide or any conductor?

The ohmic current at the surface is proportional to the tangential component of the $\vec E$ field. If the conductor is ideal, i.e., $\sigma = \infty$, then the $\vec E$ field must be perpendicular at the surface otherwise the component of the current density parallel with surface $J_t = \sigma E_t$ and consequently the dissipation would be $\infty$; the normal component of course is zero for field emission is excluded. If the conductor is not ideal this is not true anymore, and then there is nonzero parallel component of $\vec E$, see the so-called skin effect http://en.wikipedia.org/wiki/Skin_effect .