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My freshman course on waves uses Young and Freedman's University Physics. They seem to argue in the following fashion:

  • An electric field induced by a static charge distribution is conservative.

  • When all charges are at rest, the surface of a perfect conductor is thus an equipotential surface. Equivalently, the electric field is perpendicular to the surface at any point just outside the surface.

  • When an EM-wave strikes such a perfect conductor perpendicular to its surface, the electric field does have a component parallel to the surface. From the above this cannot be! But the incident wave induces oscillating currents on the surface of the conductor, which give rise to an additional EM-wave travelling in the opposite direction. The two cancel out at the surface, and the electric field is zero, so the above is obeyed.

But this doesn't seem to follow. The electric field is only conservative for static charge distributions, and they explicitly state the induction of currents on the surface of the conductor. So why must the electric field not have a component parallel to the surface?

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