Question

What is the relationship for polarisation P of a dielectric material?

Answer 1

The polarization P of a dielectric material refers to the dipole moment per unit volume within the material. When a dielectric material is placed in an electric field, its molecules or atoms become polarized, meaning the positive and negative charges within them are displaced, creating electric dipoles.

The general relationship for the polarization P is given by:

\[
P = \epsilon_0 \chi_e E
\]

Where:

1. P is the polarization (measured in Coulombs per meter cubed, C/m³).
   

1. ε₀ is the permittivity of free space (approximately \(8.854 \times 10^{-12}\, \text{C}^2 / \text{N} \cdot \text{m}^2\)).
   

1. χₑ is the electric susceptibility of the material (a dimensionless quantity that describes how easily the material becomes polarized).
   

1. E is the applied electric field (measured in volts per meter, V/m).
   

Explanation:

1. Electric Susceptibility (χₑ) tells you how responsive a material is to the electric field. Materials with higher susceptibility will polarize more strongly in response to the same electric field.
   

1. The electric field E is the external field applied to the dielectric material.
   

1. P represents the density of dipole moments that result from this applied field.
   

Alternative Relation in Terms of Permittivity:

Another way to express polarization is in terms of the relative permittivity (εᵣ) of the material:

\[
P = (\epsilon_r - 1) \epsilon_0 E
\]

Where:

1. εᵣ is the relative permittivity of the material, which is a dimensionless quantity indicating how much the material increases the capacitance compared to a vacuum.
   

1. E is the applied electric field.
   

This equation shows that the polarization depends on the relative permittivity of the material and the electric field strength.