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Inside a dielectric we have:
∇[itex]\cdot[/itex]ε0E = ρbound + ρfree , where ρbound refers to the fact that these charges come from polarization.
We can write this as:
∇[itex]\cdot[/itex]ε0E = -∇[itex]\cdot[/itex]P + ρfree
where P is the polarization of the material. And combing the two divergence terms we get:
∇[itex]\cdot[/itex]D = ρfree
which is Gauss' law for dielectrics which is quite useful sometimes. However wouldn't it only hold for solid, spherically symmetric, dielectrics, where you consider r<R. My speculation comes from the fact that this derivation does NOT consider the bound surface charges than a polarization can result in. This is of course of no problem if you are inside a solid sphere, but I don't see how it wouldn't be a problem in every other case.
∇[itex]\cdot[/itex]ε0E = ρbound + ρfree , where ρbound refers to the fact that these charges come from polarization.
We can write this as:
∇[itex]\cdot[/itex]ε0E = -∇[itex]\cdot[/itex]P + ρfree
where P is the polarization of the material. And combing the two divergence terms we get:
∇[itex]\cdot[/itex]D = ρfree
which is Gauss' law for dielectrics which is quite useful sometimes. However wouldn't it only hold for solid, spherically symmetric, dielectrics, where you consider r<R. My speculation comes from the fact that this derivation does NOT consider the bound surface charges than a polarization can result in. This is of course of no problem if you are inside a solid sphere, but I don't see how it wouldn't be a problem in every other case.