Question

What is the relationship for polarization of a dielectric material?

Answer 1

Polarization of a dielectric material refers to the alignment of the electric dipoles within the material when it is subjected to an external electric field. In simpler terms, it’s the process where the positive and negative charges inside the material get slightly separated in response to the applied electric field.

The relationship for polarization (\( P \)) can be described by the equation:

\[
P = \chi_e \epsilon_0 E
\]

Where:

1. \( P \) is the polarization vector, which measures the dipole moment per unit volume in the dielectric.
   

1. \( \chi_e \) is the electric susceptibility, a material property that measures how easily the material can be polarized.
   

1. \( \epsilon_0 \) is the permittivity of free space (a constant, approximately \( 8.854 \times 10^{-12} \, \text{F/m} \)).
   

1. \( E \) is the applied electric field.
   

How does this relate to the electric displacement field \( D \)?

The electric displacement field \( D \) is related to the electric field \( E \) and polarization \( P \) as:

\[
D = \epsilon_0 E + P
\]

This shows that \( D \) accounts for both the contribution of the free charges (in the form of \( \epsilon_0 E \)) and the induced dipoles within the dielectric (in the form of \( P \)).

Key points:

1. Polarization is the result of the material's response to an applied electric field.
   

1. The degree of polarization depends on the material's properties (like \( \chi_e \)) and the strength of the electric field.
   

1. Polarization leads to the creation of bound charges at the surfaces of the dielectric, but no net free charge is created.
   

Does that help clear things up?