Can Superposition Be Applied to a Single Charge in Different Dielectric Media?

[soupdejour]

I think I understand how superposition (of the electric field) applies for when I have two (or more) charges.

BUT, If I have only one charge, but two regions of dielectric $$\epsilon_a$$ and $$\epsilon_b$$, can I superimpose the solutions for the charge Q in just $$\epsilon_a$$ with the solution of Q in $$\epsilon_b$$?

 

[sophiecentaur]

Are you concerned with what happens at the boundary here?

 

[soupdejour]

Yes I want the boundary conditions satisfied.

 

[sophiecentaur]

OK.
When the fields were initially established, more work was done in establishing the field in one medium than in the other. That means that the energy density will be greater in one than in the other. That's if the dielectrics are in parallel.
If they are in series, the overall potential will be shared unequally across the two regions.