When does the surface charge density equal the electric flux density?

[FOIWATER]

Homework Statement

The electric field intensity in polystyrene (relative permittivity 2.55) filling the space between the plates of a parallel plate capacitor is 10kV/m. The distance between the plates is 1.5mm.
Calculate the surface charge density of free charge on the plates,
and the surface density of polarization charge

Homework Equations

rho s = D dot an

The Attempt at a Solution

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I am having a hard time seeing how the surface charge density equals the d field normal to the surface in this case?

 

[FOIWATER]

Is it because it's at a conducting surface