The relative permittivity εᵣ is, in general, a function of frequency. A medium with frequency-dependent permittivity is called dispersive. Also, the relative permittivity is a complex quantity, even in the absence of conduction σ. That is,

εᵣ(ω)= ε'(ω) - je''(ω)

The relative permittivity of a non-magnetized plasma is

εᵣ(ω)= 1 + ω²ₚ / jω(v+jω)

where ωₚ is calles the plasma frequency, and v is called the damping frequency

1. Obtain expressions for ε' and εⁿ
2.Obtain an expression for the wave number k when v =0
3. Given that Eₛ = aₓe⁻ʲᵏˢ