Physical meaning of parts of electromagnetic wave

[littlepapa87]

in

E = E_0exp i(k dot r - wt) or E = cos(k dot r - wt)

what does k dot r physically represent? Can r be any position in space or must it lie on the wave?

(I physically understand what a dot product is)

 

[Dr Lots-o'watts]

That's a plane wave, it occupies all of space.

If you want a beam that is localized along a line, E_0 has to be a function of distance from the line.

 

[jtbell]

Can r be any position in space

Yes.

or must it lie on the wave?

A 3-dimensional plane wave fills space. It doesn't lie "along" a line or other single path. See the diagram and associated instructions in the following post for a more realistic picture of a plane electromagnetic wave than you see in many textbooks.

https://www.physicsforums.com/showpost.php?p=533190&postcount=6