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What is the theory of electric polarization?
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**Electric polarization** refers to the alignment of electric dipoles (or charges) within a material in response to an applied electric field. When an electric field is applied to a material, the positive and negative charges inside the material shift slightly, causing a separation of charges. This results in an overall "polarization" of the material.

Here's a simple breakdown of how it works:

1. **What is a dipole?**
   A dipole consists of two equal and opposite charges (positive and negative) separated by a distance. For example, in water molecules, the oxygen is slightly negative, and the hydrogen atoms are slightly positive, creating a dipole.

2. **What happens when an electric field is applied?**
   When an external electric field is applied to a material, the positive and negative charges inside the material experience forces. The positive charges are pulled in the direction of the field, and the negative charges are pushed in the opposite direction.

3. **Resulting polarization:**
   This movement causes a shift in the position of the charges, aligning the dipoles in the direction of the applied electric field. The material as a whole becomes polarized.

4. **How is polarization measured?**
   The degree of polarization is often quantified by the **polarization vector** \( \mathbf{P} \), which is the dipole moment per unit volume of the material. It tells us how much the charges inside the material are displaced due to the electric field.

5. **Types of polarization:**
   There are different types of polarization, depending on the material and how it responds to the electric field:
   - **Electronic polarization**: Displacement of the electron cloud around the nucleus.
   - **Ionic polarization**: Displacement of ions in the material.
   - **Orientation polarization**: Alignment of permanent dipoles in the material.

6. **Why does this matter?**
   Electric polarization is important because it affects the material's electrical properties. For example, materials that polarize easily are often used in capacitors, where the ability to store charge is enhanced by polarization.

In simple terms: electric polarization is just the way materials rearrange their internal charges when exposed to an electric field, which influences how the material behaves electrically.
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