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We assume a perfect conductor guide, so that the atenuation is total and instantaneous and [itex]\vec{E}=0[/itex] inside the guide. But the parallel component of E is continuous at the boundary, so just outside the conductor, [itex]\vec{E}_{\parallel}=0[/itex].

But I'm thiking, this can't be a good representation of reality! Because no conductor is truly a perfect conductor. The attenuation is never total or instantaneous. In truth, [itex]\vec{E}_{\parallel}[/itex] just inside the conductor must have the same value as [itex]\vec{E}_{\parallel}[/itex] just outside of it and such a non zero value is perfectly consistent with theory.