Susceptibility and its Dimensional Formula

Susceptibility is a physical property that describes the response of a material to an applied magnetic field. It quantifies how easily a material can be magnetized when subjected to an external magnetic field. The dimensional formula of susceptibility helps express this property in terms of fundamental physical quantities.

Definition of Susceptibility

Susceptibility, denoted by χ, is defined as the ratio of the magnetization (M) produced in a material to the intensity (H) of the applied magnetic field. Mathematically, it can be expressed as:

χ = M / H

where χ is the susceptibility, M is the magnetization, and H is the magnetic field intensity.

Dimensional Formula of Susceptibility

The dimensional formula of susceptibility can be derived by considering the dimensions of magnetization and magnetic field intensity. Let's break down the dimensional formula step by step:

1. Dimensional Formula of Magnetization (M):
The dimensional formula of magnetization can be represented as [M] = [L]^[a] [M]^[b] [T]^[c], where [L], [M], and [T] represent the dimensions of length, mass, and time respectively, and 'a', 'b', and 'c' are the respective powers.

2. Dimensional Formula of Magnetic Field Intensity (H):
The dimensional formula of magnetic field intensity can be represented as [H] = [I] / [L], where [I] represents the dimension of electric current and [L] represents the dimension of length.

3. Dimensional Formula of Susceptibility (χ):
By substituting the dimensional formulas of magnetization and magnetic field intensity into the equation for susceptibility, we get:
[χ] = [M] / [H]
= [L]^[a] [M]^[b] [T]^[c] / ([I] / [L])
= [L]^[a+1] [M]^[b] [T]^[c] [I]^(-1)

Conclusion

In conclusion, the dimensional formula of susceptibility, denoted by [χ], is given by [L]^[a+1] [M]^[b] [T]^[c] [I]^(-1), where [L], [M], [T], and [I] represent the dimensions of length, mass, time, and electric current respectively. The powers 'a', 'b', and 'c' depend on the specific physical properties of the material under consideration.