So I have been introduced to the four field formalism but have not been explained it in a way that i think is logical or makes sense so i need to ask a few questions on here to allow myself to think clearly about this.
I have been told that the following relations hold:
\begin{align} \mathbf D & = \varepsilon\mathbf E \\ \mathbf H & = \frac{\mathbf B}{\mu} \end{align} where $\varepsilon = \varepsilon_0\varepsilon_r$ and $\mu = \mu_0\mu_r$.
Now consider taking an object with $\varepsilon_r = 4.0$ and placing it in an electric field of $E = 10$.
I know that to calculate the Electric field in the dielectric is $10/4 = 2.5$.
However why given the afforementioned relations are we not doing $10/4\varepsilon_0$ instead since $\varepsilon = \varepsilon_0\varepsilon_r$.
Am I wrong in thinking that D is the applied electric field and E is the electric field experienced within the dielectric? Similarly would this suggest that H is an applied magnetic field where B is something that the material feels?