I'm taking some college courses on electromagnetism and there was some talk of energy stored by electromagnetic field and its density. The expression that we use to calculate energy density stored by electric field is was $\mathbf{E \cdot D} / 2$ . However, reading my textbook it's unclear whether this expression applies to anisotropic materials too?
Answer
No it does not. The formula you wrote is valid only for isotropic material.
In general for an unit volume of material (irrespective of whether it is isotropic or not), the stored-energy is given by- $U=\int \vec{E}.d\vec{D}$
If you carryout this integral you will end up with the area under $D-E$ curve. For isotropic materials $D$ vs $E$ relation is linear therefore area under the curve is nothing but the area of the triangle (see the figure below). That gives you $U=|\vec{E}||\vec{D}|/2$. (Again, be careful about vector and its magnitude).
However energy density in non-linear medium like Ferroelectric (FE) and Antiferroelectric (AFE) is quite different.
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