polarization.md

3. Polarization and Magnetization

Electric Polarization and Displacement Field

The Electric Polarization is defined as: ^[1]

where p is the electric dipole moment and V is the volume.

Gauss's law for P is: ^[1,2]

where ρ_b is the bound charge density.

The free charge density is:

The Electric Displacement Field (in SI units) is defined as:

And apply Gauss's law for E:

Then we get Gauss's law for D:

The above equations in Gaussian units are:

From (2.1), (3.1), relation between (3.4a) and (3.4b), and , we get that:

• Electric field E:
• Electric polarization P:
• Electric displacement field D: ^[3]
• Electric displacement flux Φ_D: (1/4π to the electric charge conversion)

Magnetization and H Field

The Magnetization is defined as: ^[1]

where m is the magnetic dipole moment and V is the volume.

The magnetization current density (in SI unit) is: ^[4]

The total current density is:

where J_p is the polarization current density: ^[1]

The Magnetic H Field (in SI units) is defined as:

And apply Ampère-Maxwell Equation for B:

Then we get Ampère-Maxwell equation for H: ^[5]

The above equations in Gaussian units are:

From (2.4), relation between (3.5a) and (3.5b), relation between (3.8a) and (3.8b), and , we get that:

• Magnetic B field:
• Magnetization M: ^[6]
• Magnetic H field: ^[6]

Notes

1. These always hold in all unit systems.
2. Here is the explanation.
3. Here is the calculation.
4. Refer to here.
5. Here is the proof.
6. Here are the calculations.