1 Answer
The polarization P of an electric field is the dipole moment per unit volume in a dielectric material. It is related to the electric field E and the electric displacement field D. The general formula for polarization is:
\[
\mathbf{P} = \epsilon_0 (\chi_e) \mathbf{E}
\]
Where:
Alternatively, polarization can also be expressed using the relationship between the electric displacement field \(\mathbf{D}\) and the electric field \(\mathbf{E}\) as:
\[
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
\]
From this, we can solve for polarization:
\[
\mathbf{P} = \mathbf{D} - \epsilon_0 \mathbf{E}
\]
This formula shows that the polarization is the difference between the electric displacement field and the contribution from the free space electric field.
\[
\mathbf{P} = \epsilon_0 (\chi_e) \mathbf{E}
\]
Where:
- \(\mathbf{P}\) is the polarization vector (Coulombs per meter squared, C/m²).
- \(\epsilon_0\) is the permittivity of free space (approximately \(8.85 \times 10^{-12}\) C²/(N·m²)).
- \(\chi_e\) is the electric susceptibility of the material (dimensionless).
- \(\mathbf{E}\) is the electric field vector (Volts per meter, V/m).
Alternatively, polarization can also be expressed using the relationship between the electric displacement field \(\mathbf{D}\) and the electric field \(\mathbf{E}\) as:
\[
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
\]
From this, we can solve for polarization:
\[
\mathbf{P} = \mathbf{D} - \epsilon_0 \mathbf{E}
\]
This formula shows that the polarization is the difference between the electric displacement field and the contribution from the free space electric field.