# I Uniform polarization and linear dielectrics

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1. Aug 12, 2017

### Pushoam

Can a sphere with a frozen - in uniform polarization $\vec P$ be considered a linear dielectrics?

Following the definition of dielectrics given in Griffiths:

The electric field inside the sphere,
$\vec E = \frac {-P}{3 \epsilon_0}$
So, $\vec P ≠ ε_0 χ_e \vec E$ as $ε_0 χ_e$ can't be negative?

On the other hand, outside the dielectrics, $\vec P is 0$ , but $\vec E is non-zero$ and $ε_0 χ_e$ can't be 0.
Hence, acc. to eq. 4.30,
A sphere with uniform polarization is not linear dielectrics.
Is this correct?

2. Aug 12, 2017

There are cases of spontaneous polarization $\vec{P}$ in the absence of an electric field. I believe these materials are known as ferroelectrics. In general, you can not assign a dielectric constant to this spontaneous polarization. I believe what you have concluded is also correct=when in the shape of a sphere, the material inside will still retain the spontaneous polarization, and will not be appreciably affected by the electric field due to the surface polarization charge that has an electric field opposite the polarization of $\vec{E}_p=-\vec{P}/(3 \epsilon_o )$.