Question

What is the formula for permeability and permittivity?

Answer 1

Permeability (\(\mu\)) and permittivity (\(\epsilon\)) are fundamental properties of materials that influence how electric and magnetic fields interact with them.

1. Permeability (\(\mu\)):  
   

   Permeability describes how a material responds to a magnetic field. It is the measure of the material's ability to support the formation of a magnetic field within itself.

   The formula for the permeability of free space (vacuum) is:
   \[
   \mu_0 = 4\pi \times 10^{-7} \, \text{N/A}^2
   \]
   Where:
   - \(\mu_0\) is the permeability of free space (vacuum).
   
   The permeability of a material is given by:
   \[
   \mu = \mu_0 \times \mu_r
   \]
   Where:
   - \(\mu\) is the permeability of the material,
   - \(\mu_0\) is the permeability of free space,
   - \(\mu_r\) is the relative permeability (a dimensionless constant specific to the material).

1. Permittivity (\(\epsilon\)):  
   

   Permittivity describes how a material responds to an electric field, or in simpler terms, how well it allows electric field lines to pass through.

   The formula for the permittivity of free space (vacuum) is:
   \[
   \epsilon_0 = 8.854 \times 10^{-12} \, \text{F/m}
   \]
   Where:
   - \(\epsilon_0\) is the permittivity of free space.

   The permittivity of a material is given by:
   \[
   \epsilon = \epsilon_0 \times \epsilon_r
   \]
   Where:
   - \(\epsilon\) is the permittivity of the material,
   - \(\epsilon_0\) is the permittivity of free space,
   - \(\epsilon_r\) is the relative permittivity (also called the dielectric constant) of the material.

In summary:

1. Permeability (\(\mu\)) relates to the magnetic response of a material.
   

1. Permittivity (\(\epsilon\)) relates to the electric response of a material.
   

Both depend on the properties of the material, and their values in vacuum are constants (\(\mu_0\) and \(\epsilon_0\)), while for materials, they vary depending on their composition.