What is the Relationship between E, D and P in a Material?

[Roodles01]

A problem involving E, D & P. I have the answer but not sure why for the P bit.A bit of clarification if someone could, please.

A thick sheet of polystyrene, of relative permittivity ε = 2.5, is placed
normal to a uniform electric field of magnitude 500Vm⁻¹ in air.

Find the magnitudes of the electric field E, the electric displacement D and the polarization P inside the material.

OK div D = ρ_f
and D = εε₀E
Boundary conditions D_outside = D_inside → ε_outE_out = εε₀E_in

so
E_in = E_out / ε
E_in = 500/2.5
E_in = 200 Vm^-1

D_out = D_in = ε₀ E_out
D_out = 8.85x10^-12 x 200
D_out = 1.77x10^-9


Fine so far . . .

When I get down to calculating P I have to use

D_in = ε₀E_in + P_in

why, when everything else has the suffix "in" do I use ε₀? Shouldn't it be just plain ε?

Thanks in advance.

 

[Greg Bernhardt]

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