Can there be a material with relative permittivity < 1?

[x_engineer]

Just a thought experiment...

Cover a metal plate with a material of relative permittivity 0 on one side. Then place a charge on the metal plate. The system as a whole will accelerate towards the metal side since there is no flux on the covered side and so the charge is accelerated in the direction of the uncovered side. This is a violation of the conservation of energy principle, so it is impossible.

Extending the argument to relative permittivity simply less than one instead of 0, there will be less flux on the covered side, so again the charge is accelerated in the direction of the uncovered side. So this must also not be possible.

But we do have materials with relative permittivity greater than one, and I could use the same argument in that case. Why can I not, or why is it invalid to extend the argument for 0 permittivity to finite permittivity?

 

[chipmunk24]

Your argument is slightly wrong, as you have realized from the fact that its extension would require violation of conservation of energy for any substance with k>1 or k<1. Imagine your plate is exceptionally large, to make edge effects negligible, and in free space, with a charge per unit area Q on it. By symmetry the field lines are perpendicular to the surface, and by Gauss' Law the E flux through an area A parallel to the plate is QA/2e, where e is the permittivity, so E is Q/2e. Now if you change the permittivity of the region beyond some perpendicular distance from the plate to e', then E= Q/2e'. This means that field lines have come out of nowhere, which would seem to be in violation of Gauss' Law. The reason is that they emerge from the surface charge on the polarised dielectric material with the different e. For all materials I know of, this polarization is in the opposite direction to the applied field, because the positive charges in the material are attracted to the negative potential and vice-versa. This appears as a higher-than-unity dielectric constant. However, some material with a lower-than-one or even negative permittivity would have to align negative charges at the negative potential, and vice-versa, requiring an energy input, which is why nothing I have ever heard of behaves like this.
Therefore, it is the effects of the polarization of the dielectric that explains this confusion.