as the permeability of a material is the ratio of the magnetic field strength and the magnetic flux, could the permeability of the material be multiplied by the magnetic field strength in order to calculate the flux?

No, you cannot directly multiply the permeability of a material by the magnetic field strength to calculate the magnetic flux. The permeability of a material is a property that describes how easily magnetic flux passes through it. It is represented by the symbol μ (mu) and is measured in units of Henry per meter (H/m) in the International System of Units (SI).

The relationship between magnetic field strength (H), magnetic flux (Φ), and permeability (μ) is given by the equation:

Φ = B * A * μ

where B represents the magnetic field strength, A represents the cross-sectional area perpendicular to the magnetic field, and Φ represents the magnetic flux passing through that area.

To calculate the magnetic flux, you need to know the magnetic field strength, the cross-sectional area, and the permeability of the material. You can rearrange the equation to solve for the magnetic flux:

Φ = (B * A) / μ.

So, you divide the product of the magnetic field strength and the cross-sectional area by the permeability to calculate the magnetic flux.

Note that in certain circumstances, such as when working with a vacuum or air, the permeability is equal to a constant value called the permeability of free space, μ₀ (mu naught), which is approximately equal to 4π × 10⁻⁷ H/m. In such cases, the equation simplifies to:

Φ = (B * A) / (μ₀).

Remember to use the appropriate value for the permeability depending on the material you are dealing with.