Reluctance is inversely proportional to the area of cross section of the material.

Reluctance is a property of a material that opposes the flow of magnetic flux. It is analogous to resistance in an electrical circuit. The higher the reluctance, the more difficult it is for the magnetic flux to pass through the material.

Explanation:
To understand why reluctance is inversely proportional to the area of cross section, let's consider the formula for reluctance:

Reluctance (S) = (length of the magnetic path)/(μ₀ * permeability * area of cross section)

Where:
- Length of the magnetic path is the distance the magnetic flux travels through the material
- μ₀ is the permeability of free space (a constant)
- Permeability is the measure of a material's ability to conduct magnetic flux
- Area of cross section is the area perpendicular to the direction of magnetic flux

From the formula, we can see that the reluctance is directly influenced by the length of the magnetic path, permeability, and inversely influenced by the area of cross section.

Impact of Area of Cross Section:
When the area of cross section is increased, the reluctance decreases. This is because a larger area provides more space for the magnetic flux to pass through the material, resulting in a lower opposition to the flow of flux. Conversely, when the area of cross section is decreased, the reluctance increases as there is less space for the flux to pass through, leading to a higher opposition.

Example:
Let's consider a simple example to illustrate this relationship. Suppose we have two materials with the same length of magnetic path and the same permeability. However, one material has a larger area of cross section compared to the other.

- Material A: Area of cross section = 10 cm²
- Material B: Area of cross section = 5 cm²

Since reluctance is inversely proportional to the area of cross section, Material A will have a lower reluctance compared to Material B. This means that Material A will allow the magnetic flux to pass through more easily than Material B.

Conclusion:
In summary, reluctance is inversely proportional to the area of cross section. Increasing the area of cross section decreases the reluctance, allowing for easier passage of magnetic flux through the material. Conversely, decreasing the area of cross section increases the reluctance, making it more difficult for the flux to pass through.