EM wave - nodes at metal surface

[Edgardo]

I've read in a book, that if you had a standing electromagnetic wave between two metal plates, only nodes would be at the metal plates. This is due to the infinite high conduction of metal, the book says.

Why is that so?

 

[Galileo]

This is one of the boundary conditions of an electric field at the surface of a conductor. Inside the conductor, the electric field will be zero since any electric field will cause the charges to move around as to cancel this field (practically instantaneously).
Same reasoning applies with the wave. Any E-field at the surface of the metal plate will cause the electrons to move around as to cancel this field. So it will always be zero.

 

[Edgardo]

So the E-field (and the B-field) at the surface is zero, since the electrons' movements cancel out the E-field? And the movement is so fast that it is really zero?

 

[Galileo]

Yes, it is practically instantaneous. Mathematically it IS in the case of an ideal conductor.
Any field in, say, the x-direction will push on the charges and cause positive to accumulate x direction and negative charge in the -x direction. This arrangement will produce its own field in the -x direction as to cancel the original field, so the total field will be zero.

 

[Meir Achuz]

It is only the component of E parallel to the metal'surface that is zero. The component perpendicular to (and just outside) the surface is not zero. For B, it is the opposite. The normal component is zero and the tangential component is not. If the wave vector (k) is perpendicular to the surface, E at the surface is zero, but B is not.