Magnetic Flux Density (B) and Magnetic Susceptibility (χ)

Magnetic flux density (B) is a measure of the strength of a magnetic field. It represents the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field.

Magnetic susceptibility (χ) is a property of materials that describes how easily they can be magnetized in the presence of an external magnetic field.

Magnetization (M)

Magnetization (M) represents the magnetic moment per unit volume of a material. It indicates how strongly a material is magnetized when exposed to an external magnetic field.

Formula

The relationship between magnetic flux density (B), magnetic susceptibility (χ), and magnetization (M) is given by the equation:

B = μ₀(H + M)

where μ₀ is the permeability of free space and H is the magnetic field strength.

Conversion

To find the magnetization (M), we need to rearrange the equation as follows:

M = (B - μ₀H) / μ₀

Solution

Given:
- Magnetic flux density (B) = 0.02 Wb/m²
- Magnetic susceptibility (χ) = 0.003

We know that μ₀ = 4π x 10⁻⁷ Tm/A

First, we need to find the magnetic field strength (H) using the formula:

H = B / μ₀ - M

Substituting the given values:

H = 0.02 / (4π x 10⁻⁷) - M

Next, we can rearrange the formula for magnetization (M) and solve for it:

M = (B - μ₀H) / μ₀

Substituting the values of B and H:

M = (0.02 - (4π x 10⁻⁷)H) / (4π x 10⁻⁷)

Now, we can substitute the value of χ into the equation:

M = (0.02 - (4π x 10⁻⁷)H) / (4π x 10⁻⁷ x 0.003)

Simplifying the equation:

M = (0.02 - (4π x 10⁻⁷)H) / (12π x 10⁻¹⁰)

Finally, we can substitute the value of H from the previously calculated equation and solve for M:

M = (0.02 - (4π x 10⁻⁷) x (0.02 / (4π x 10⁻⁷))) / (12π x 10⁻¹⁰)

M = (0.02 - 0.02) / (12π x 10⁻¹⁰)

M = 0 / (12π x 10⁻¹⁰)

M = 0 A/m

Therefore, the correct answer is option 'A' (47.6 A/m).