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**1. Homework Statement**

Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that:

D(1)-D(2)=free surface charge density=s

where D(1) is the component of the first medium normal to the surface.

But suppose that there's nothing else apart from two infinite dielectrics with a constant free charge density between then, how would I work out what the actual values of D(1) and D(2) are rather than just the difference?

**3. The Attempt at a Solution**

It seems reasonable that the D field should be the same on both sides so that D=s/2 but I'm not sure how I'd prove this?

Any help appreciated.