How to model the impedance of a coil with a dielectric slab on the top I have sketched what I meant in the image below. Were there no dielectric slab, the coil could have been simply modeled as an inductor. But I am not sure what the impedance can be if there is a dielectric slab next to or not far from one end of the coil. 

 A: I think this simple question is an excellent one. 
The simple answer is: if the slab has the same magnetic constant as freespace, i.e. $\mu_0$, it has negligible effect on the inductor if the frequency is low enough that the problem can be thought of as magnetostatic. 
I'm not sure how well wonted Maxwell's equations are to you, but the criterion that you need to look at to tell whether the problem is magnetostatic is whether the displacement current term in Ampère's law is negligible compared to the conduction current. Generally this can be replaced by whether the inductor is small compared to the wavelength of EM radiation at the working frequency. At high frequencies, changing electric fields induce magnetic ones, so the electric field induced by the changing magnetic flux through the inductor in turn bears on the magnetic flux in the inductor. 
You will work out the inductance of a solenoid by applying Ampère's law to a loop running down the axis of the solenoid, stradling the windings and making its way back to its beginning outside the inductor. Then we have:
$$\oint_\mathscr{L} \vec{H}\cdot{\rm d}\,\vec{r} = \mu_0\,N\,I + \epsilon\,\frac{\partial}{\partial\,t}\,\Phi_E$$
where $\mathscr{L}$ is the textbook loop used to derive the solenoid's inductance and $\Phi_E$ is the flux trough this loop of the electric field induced, as described by Faraday's Law, by the changing magnetic fiel. When the frequency is low, the second term on the right is very small, and there is thus no way for the electric constants of the materials involved to influence the magnetic field.
