[Physics] the physical reasons for variations in the tangential and normal components in Dielectric to Dielectric Boundary conditions

Question

According to Dielectric to Dielectric Boundary conditions, the tangential components of the
electric field E remain continuous at the boundary of two dielectrics while the tangential
component of electric flux density D is discontinuous. Furthermore, the normal components
of the electric flux density D remain continuous at the boundary of two dielectrics while the
normal component of electric field E is discontinuous. How can we explain this phenomenon physically?

Answer 1

In Maxwell Equations for the electric field, we have that: $$ \nabla \times E = - \partial B / \partial t $$ $$ \nabla \cdot E = \rho /\epsilon_0 $$ and you can define the electric flux density as: $$ D = \epsilon E $$ with $\epsilon$ dielectric constant of that medium (for a more detailed and physical definition, take a look here) . You can then demonstrate, as done here the condition for each field. You have then that if you demonstrated for instance the conservation of the tangential component of E: $$ E_{t1} = E_{t2} \rightarrow D_{t1} ε_1 = D_{t2} ε_2 \rightarrow D_{t1} \neq D_{t2} $$ since at an interface $ε_1 \neq ε_2$. The same can be done for the normal component of D.