Approximate a plane E&M wave with this large sum....

[Spinnor]

I would like to approximate a plane electromagnetic wave with a very large sum of the following.

Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by,

P(z,t) = pcos(kz-ωt). The polarization is a function of both space and time. Now let there be a uniform density of such lines in all space all parallel to one another, all in phase, and with them all polarized in the x direction. Will such a construction approximate the electric and magnetic fields of plane E&M wave?

Thanks!

 

[tech99]

I would like to approximate a plane electromagnetic wave with a very large sum of the following.

Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by,

P(z,t) = pcos(kz-ωt). The polarization is a function of both space and time. Now let there be a uniform density of such lines in all space all parallel to one another, all in phase, and with them all polarized in the x direction. Will such a construction approximate the electric and magnetic fields of plane E&M wave?

Thanks!

I just cannot understand the question. How can we have polarisation on that line and also perpendicular to it?

 

[Spinnor]

I just cannot understand the question. How can we have polarisation on that line and also perpendicular to it?

Just imagine at each point of the line a polarization vector that is also perpendicular to the line. Polarization is charge times a distance, just imagine the distance is very small, as small as you wish with charge increased so that distance times charge is a constant. Let the distance be of order the string length in string theory, that is pretty damn small.

Sorry for the confusion.