Question
How does the electric field inside a dielectric decrease when it is placed in an external electric field?

Answer

Suppose a rectangular slab of dielectric is placed in an electric field $\overrightarrow{E_0}$, with two of its parallel sides perpendicular to the field. The dielectric becomes polarized. Polarization charges appear on the external surfaces of these two parallel sides such that within the dielectric the field due to the polarization charges is opposite to $\overrightarrow{E_0}$. Thus, the magnitude of the net electric field $\vec{E}$ within the dielectric is less than $\left|\overrightarrow{E_0}\right| \cdot E=\frac{E_0}{k}$, where $k$ is the relative permittivity (dielectric constant) of the dielectric.

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