Question

What is the relationship between permeability and susceptibility?

Answer 1

Permeability (μ) and susceptibility (χ) are both related to how a material responds to a magnetic field, but they are different concepts. Here's how they are connected:

1. Permeability (μ):
   

   - Permeability is a measure of how easily a material can become magnetized when exposed to a magnetic field.
   - It tells you how much magnetic field can pass through a material. A high permeability means the material can support a strong magnetic field.

1. Magnetic Susceptibility (χ):
   

   - Susceptibility is a measure of how much a material will become magnetized in response to an external magnetic field.
   - It indicates the degree to which a material is "susceptible" to magnetization when exposed to a magnetic field. Materials with high susceptibility become strongly magnetized.

Relationship:

The relationship between permeability (μ) and susceptibility (χ) is given by the following formula:

\[
\mu = \mu_0 (1 + \chi)
\]

Where:

1. \(\mu_0\) is the permeability of free space (a constant value, approximately \(4\pi \times 10^{-7} \, \text{H/m}\)).
   

1. \(\mu\) is the permeability of the material.
   

1. \(\chi\) is the magnetic susceptibility of the material.
   

This equation shows that permeability is directly related to susceptibility. Specifically:

1. If the material has a high susceptibility, its permeability will be higher, meaning it allows a stronger magnetic field to pass through.
   

1. If the material has a low susceptibility, its permeability will be closer to the permeability of free space.
   

Key points:

1. Permeability (μ) refers to how well a material can support a magnetic field.
   

1. Susceptibility (χ) measures how much a material responds to the magnetic field.
   

1. The two are related through the formula: \(\mu = \mu_0 (1 + \chi)\).
   

So, if you know the magnetic susceptibility of a material, you can calculate its permeability!